Cabozantinib S-Malate in Treating Patients With Advanced Solid Tumors and Human Immunodeficiency Virus

Inclusion Criteria:

* Participants must have known HIV infection and histologically confirmed solid malignancy that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective; any number of prior cancer therapies will be permitted; at least 4 weeks must have elapsed since prior chemotherapy or biological therapy, 6 weeks if the regimen included carmustine (BCNU) or mitomycin C; prior radiation therapy to the thoracic cavity, abdomen, or pelvis must be completed at least 3 months prior to registration; radiotherapy to any other site (including bone or brain metastases) must be completed at least 28 days prior to registration
* Serologic documentation of HIV infection at any time prior to study entry, as evidenced by positive enzyme-linked immunosorbent assay (ELISA), positive western blot, or any other federally approved licensed HIV test; alternatively, this documentation may include a record that another physician has documented that the participant has HIV infection based on prior ELISA and western blot, or other approved diagnostic tests
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)
* Life expectancy of greater than 12 weeks
* Leukocytes \>= 3,000/mcL (within 1 week of study entry)
* Absolute neutrophil count \>= 1,500/mcL (within 1 week of study entry)
* Platelets \>= 100,000/mcL (within 1 week of study entry)
* Total bilirubin=\< 1.5 x upper limit of normal (ULN) (within 1 week of study entry) (if, however, the participant has Gilbert's disease or unconjugated hyperbilirubinemia that is considered to be secondary to with atazanavir or indinavir therapy, then the total bilirubin must be =\< 3 x ULN)
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3.0 x institutional upper limit of normal (within 1 week of study entry)
* Creatinine =\< 1.5 x ULN (within 1 week of study entry)
* Creatinine clearance \>= 50 mL/min/1.73 m\^2 for participants with creatinine levels above institutional normal (within 1 week of study entry)
* Hemoglobin \>= 9 g/dL (within 1 week of study entry)
* Serum albumin \>= 2.8 g/dL (within 1 week of study entry)
* Lipase \< 2.0 x ULN and no radiologic or clinical evidence of pancreatitis (within 1 week of study entry)
* Urine protein/creatinine ratio (UPCR) =\< 1 (within 1 week of study entry)
* Serum phosphorus \>= lower limit of normal (LLN) (within 1 week of study entry)
* Calcium \>= LLN (within 1 week of study entry)
* Magnesium \>= LLN (within 1 week of study entry)
* Potassium \>= LLN (within 1 week of study entry)
* A cluster of differentiation (CD)4+ lymphocyte count \> 50/mcL will be required within 2 weeks of study participation
* Women of childbearing potential must have a negative pregnancy test within 7 days before enrollment; women of childbearing potential include women who have experienced menarche and who have not undergone successful surgical sterilization (hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or are not postmenopausal; postmenopause is defined as amenorrhea \>= 12 consecutive months; note: women who have been amenorrheic for 12 or more months are still considered to be of childbearing potential if the amenorrhea is possibly due to prior chemotherapy, antiestrogens, ovarian suppression or any other reversible reason
* The effects of cabozantinib on the developing human fetus are unknown; for this reason and because tyrosine kinase inhibitors agents as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately; men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 6 months after completion of cabozantinib administration; sexually active participants (men and women) must agree to use medically accepted barrier methods of contraception (e.g., male or female condom) during the course of the study and for 6 months after the last dose of study drug(s), even if oral contraceptives are also used; all participants of reproductive potential must agree to use both a barrier method and a second method of birth control during the course of the study and for 6 months after the last dose of study drug
* Participating participants MUST receive appropriate care and treatment for HIV infection, including antiretroviral medications, when clinically indicated and should be under the care of a physician experienced in HIV management; participants will be eligible regardless of antiretroviral medication (including no antiretroviral medication) provided there is no intention to initiate therapy or the regimen has been stable for at least 4 weeks with no intention to change the regimen within 8 weeks following study entry; as study-specific (antiretroviral-based) strata fill, however, only participants who are receiving the therapies eligible for the remaining open strata will be accrued
* Ability to understand and the willingness to sign a written informed consent document
* Participants must in the opinion of the investigator be capable of complying with this protocol

Exclusion Criteria:

* Prior treatment with cabozantinib (XL184)
* The participant has received radionuclide treatment within 6 weeks of the first dose of study treatment
* The participant has received prior treatment with a small molecule kinase inhibitor or a hormonal therapy (including investigational kinase inhibitors or hormones) within 4 weeks or five half-lives of the compound or active metabolites, whichever is longer, before the first dose of study treatment; note: participants with prostate cancer currently receiving luteinizing hormone-releasing hormone (LHRH) or gonadotropin-releasing hormone (GnRH) agonists may be maintained on these agents
* The participant has received any other type of investigational agent within 28 days before the first dose of study treatment
* The participant has not recovered to baseline or Common Terminology Criteria for Adverse Events (CTCAE) =\< grade 1 from toxicity due to all prior therapies except alopecia and other non-clinically significant adverse events (AEs)
* The participant has a primary brain tumor
* The participant has active brain metastases or epidural disease; participants with brain metastases previously treated with whole brain radiation or radiosurgery or participants with epidural disease previously treated with radiation or surgery who are asymptomatic and do not require steroid treatment for at least 4 weeks before starting study treatment are eligible; participants with treated brain metastasis should not take enzyme-inducing anticonvulsive therapies (EIACDs) within 2 weeks of registration, though non-enzyme inducing anticonvulsive drugs such as levetiracetam are allowed; neurosurgical resection of brain metastases or brain biopsy is permitted if completed at least 3 months before starting study treatment; baseline brain imaging with contrast-enhanced computed tomography (CT) or magnetic resonance imaging (MRI) scans for participants with known brain metastases is required to confirm eligibility
* The participant has prothrombin time (PT)/international normalized ratio (INR) or partial thromboplastin time (PTT) test \>= 1.3 x the laboratory ULN within 7 days before the first dose of study treatment
* The participant requires concomitant treatment, in therapeutic doses, with anticoagulants such as warfarin or warfarin-related agents, heparin, thrombin or factor xabans (Xa) inhibitors, or antiplatelet agents (e.g., clopidogrel); low dose aspirin (=\< 81 mg/day), low-dose warfarin (=\< 1 mg/day), and prophylactic low molecular weight heparin (LMWH) are permitted
* The participant requires chronic concomitant treatment with the following strong cytochrome P450 family 3, subfamily A, polypeptide 4 (CYP3A4) inducers OTHER than antiretroviral agents: dexamethasone, phenytoin, carbamazepine, rifampin, rifabutin, rifapentine, phenobarbital, primidone, modafinil, and other enzyme inducing anti-convulsant drugs (EIACD), and St. John's wort; use of efavirenz or etravirine is permitted for participants considered for the CYP3A4-inducer based antiretroviral therapy (ART) regimen arm (Stratum B) of the trial; because the lists of CYP3A4 inducers are constantly changing, it is important to regularly consult a frequently-updated list; medical reference texts such as the Physicians' Desk Reference may also provide this information; as part of the enrollment/informed consent procedures, the participant will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the participant is considering a new over-the-counter medicine or herbal product
* The participant requires concomitant treatment with the following inhibitors of CYP3A4:

  * Antibiotics: clarithromycin, erythromycin, telithromycin, troleandomycin
  * Antifungals: itraconazole, ketoconazole, voriconazole, fluconazole, posaconazole
  * Antidepressants: nefazodone
  * Antidiuretic: conivaptan
  * Gastrointestinal (GI): cimetidine, aprepitant
  * Hepatitis C: boceprevir, telaprevir
  * Miscellaneous: Seville oranges, grapefruit, or grapefruit juice and/or pummelos, star fruit, exotic citrus fruits, or grapefruit hybrids); use of any of anti-retrovirals (delavirdine) or protease inhibitors (ritonavir, indinavir, lopinavir/ritonavir, saquinavir, nelfinavir) is permitted; specifically, ritonavir and cobicistat is permitted for participants considered for the CYP3A4-inhibitor based ART regimen arm (Stratum A) of the trial; because the lists of CYP3A4 inhibitors are constantly changing, it is important to regularly consult a frequently-updated list; medical reference texts such as the physicians' desk reference may also provide this information; as part of the enrollment/informed consent procedures, the participant will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the participant is considering a new over-the-counter medicine or herbal product
* The participant has experienced any of the following:

  * Clinically-significant gastrointestinal bleeding within 6 months before the first dose of study treatment
  * Hemoptysis of \>= 0.5 teaspoon (2.5 mL) of red blood within 3 months before the first dose of study treatment
  * Any other signs indicative of pulmonary hemorrhage within 3 months before the first dose of study treatment
* The participant has radiographic evidence of cavitating pulmonary lesion(s)
* The participant has tumor invading or encasing any major blood vessels
* The participant has uncontrolled, significant intercurrent or recent illness including, but not limited to, the following conditions:

  * Cardiovascular disorders including:

    * Congestive heart failure (CHF): New York Heart Association (NYHA) class III (moderate) or class IV (severe) at the time of screening
    * Concurrent uncontrolled hypertension defined as sustained blood pressure (BP) \> 140 mmHg systolic, or \> 90 mmHg diastolic despite optimal antihypertensive treatment within 7 days of the first dose of study treatment
    * Any history of congenital long QT syndrome
    * Any of the following within 6 months before the first dose of study treatment:

      * Unstable angina pectoris
      * Clinically-significant cardiac arrhythmias
      * Stroke (including transient ischemic attack \[TIA\], or other ischemic event)
      * Myocardial infarction
      * Thromboembolic event requiring therapeutic anticoagulation (note: participants with a venous filter \[e.g. vena cava filter\] are not eligible for this study)
  * Gastrointestinal disorders particularly those associated with a high risk of perforation or fistula formation including:

    * Any of the following within 28 days before the first dose of study treatment

      * Active peptic ulcer disease
      * Inflammatory bowel disease (including ulcerative colitis and Crohn's disease), diverticulitis, cholecystitis, symptomatic cholangitis or appendicitis
      * Malabsorption syndrome
    * Any of the following within 6 months before the first dose of study treatment:

      * Abdominal fistula
      * Gastrointestinal perforation
      * Bowel obstruction or gastric outlet obstruction
      * Intra-abdominal abscess; note: complete resolution of an intra-abdominal abscess must be confirmed prior to initiating treatment with cabozantinib even if the abscess occurred more than 6 months before the first dose of study treatment
* Other disorders associated with a high risk of fistula formation including percutaneous endoscopic gastrostomy (PEG) tube placement within 3 months before the first dose of study therapy
* Other clinically significant disorders such as:

  * Active infection requiring systemic treatment within 28 days before the first dose of study treatment; participants with HIV infection will be eligible provided they meet the criteria; participants with known hepatitis B infection should be screened for active disease prior to study participation; participants with known hepatitis C infection must not be actively receiving treatment for the infection
  * Serious non-healing wound/ulcer/bone fracture within 28 days before the first dose of study treatment
  * History of organ transplant
  * Concurrent uncompensated hypothyroidism or thyroid dysfunction within 7 days before the first dose of study treatment
  * History of major surgery as follows:

    * Major surgery within 3 months of the first dose of cabozantinib if there were no wound healing complications or within 6 months of the first dose of cabozantinib if there were wound complications
    * Minor surgery within 1 month of the first dose of cabozantinib if there were no wound healing complications or within 3 months of the first dose of cabozantinib if there were wound complications
  * In addition, complete wound healing from prior surgery must be confirmed at least 28 days before the first dose of cabozantinib irrespective of the time from surgery
* The participant is unable to swallow tablets that are whole (do not crush or chew or administer via nasogastric \[NG\]-tube)
* The participant has a corrected QT interval calculated by the Fridericia formula (QTcF) \> 500 ms within 28 days before randomization; note: if initial QTcF is found to be \> 500 ms, two additional electrocardiogram (ECGs) separated by at least 3 minutes should be performed; if the a