Cabozantinib-S-Malate and Vemurafenib in Treating Patients With Solid Tumors or Melanoma That is Metastatic or That Cannot Be Removed By Surgery

Inclusion Criteria:

* Patients entered on the dose-escalation portion of the trial must have a histologically confirmed solid tumor malignancy that is metastatic or unresectable and molecularly confirmed to harbor a mutation in v-raf murine sarcoma viral oncogene homolog (BRAF) at V600
* Patients entered on the dose expansion portion of the study must have histologically and molecularly confirmed malignant melanoma that is metastatic or unresectable and found to be harbor a mutation in BRAF at V600
* Patients in the dose escalation portion of the study may have had none or any number of prior therapies
* Patients in the dose expansion portion may have any number of prior therapies but must have been treated with a selective BRAF inhibitor (including but not necessarily limited to vemurafenib, trametinib, Raf kinase inhibitor LGX818 \[LGX818\]) as their prior line of therapy, and had documented stable disease for at least 4 months or disease progression, as interpreted by the accruing investigator; there is no minimum period of treatment with a BRAF inhibitor required prior to determination of progression; documentation of progression on a selective BRAF inhibitor may not have taken place more than 1 month prior to enrollment on this study
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)
* Leukocytes \>= 3,000/mcL
* Absolute neutrophil count \>= 1,000/mcL
* Platelets \>= 100,000/mcL
* Total bilirubin =\< 1.5 × upper limit of normal (ULN)
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3.0 × institutional upper limit of normal
* Creatinine =\< 1.5 × ULN OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal
* Hemoglobin \>= 9 g/dL
* Serum albumin \>= 2.5 g/dL
* Lipase \< 2.0 × ULN and no radiologic or clinical evidence of pancreatitis
* Urine protein/creatinine ratio (UPCR) =\< 1
* Serum phosphorus calcium \>= lower limit of normal (LLN)
* Serum magnesium \>= LLN
* Serum potassium \>= LLN
* Women of childbearing potential must have a negative pregnancy test at screening; 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; post-menopause 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, anti-estrogens, ovarian suppression or any other reversible reason
* 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 4 months after completion of XL184 administration; all subjects 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 4 months after the last dose of study drug(s)
* Patients to be enrolled in the maximum tolerated dose (MTD) dose expansion portion of the study must have progressive measurable disease (excluding central nervous system \[CNS\]-only based disease) prior to the administration of study treatment
* Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

* Prior treatment with XL184 (cabozantinib) or other mesenchymal-epithelial transition (MET) directed therapy
* The subject has received radiation therapy:

  * To the thoracic cavity, abdomen, or pelvis within 3 months before the first dose of study treatment, or has ongoing complications, or is without complete recovery and healing from prior radiation therapy
  * To bone metastasis within 14 days before the first dose of study treatment
* The subject has received radionuclide treatment within 6 weeks of the first dose of study treatment
* The subject has not recovered to baseline or Common Terminology Criteria for Adverse Events (CTCAE) =\< grade 1 from toxicity due to all prior therapies except alopecia, rash, and other non-clinically significant adverse events (AEs)
* The subject has unstable brain metastases or epidural disease; subjects with brain metastases who are treated with whole brain radiation or radiosurgery or subjects with epidural disease previously treated with radiation or surgery who are asymptomatic following treatment and do not require steroid treatment for 2 weeks before starting study treatment are eligible (BRAF inhibitor should be continued through this period if possible); 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 subjects with known brain metastases is required to confirm eligibility; the use of anti-convulsant medications are allowed only if these are non-enzyme inducing anti-epileptic agents (NEIAED) including but not limited to valproate, benzodiazepines, gabapentin, lamotrigine, levetiracetam, tiagabine and zonisamide
* The subject 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 subject 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 subject requires chronic concomitant treatment of strong cytochrome P450 family 3, subfamily A, polypeptide 4 (CYP3A4) inducers (e.g., dexamethasone, phenytoin, carbamazepine, rifampin, rifabutin, rifapentine, phenobarbital, and St. John's Wort); as part of the enrollment/informed consent procedures, the patient 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 patient is considering a new over-the-counter medicine or herbal product; concomitant medications that are primarily metabolized by the cytochrome P450 (CYP450) ) family 1, subfamily A, polypeptide 2 (1A2), 3A4 and family 2, subfamily C, polypeptide 9 (2C9) as well as those that strongly inhibit or induce CYP3A4 should be used with caution with vemurafenib; the categories of drugs listed below if used, should be monitored with caution for potential alterations in drug exposure and toxicity

  * Non-steroidal anti-inflammatory drugs (NSAIDs) (e.g., ibuprofen, diclofenac, meloxicam)
  * Oral hypoglycemic agents (e.g., tolbutamide, glipizide, glyburide, glimepiride)
  * Antihypertensives (e.g., losartan, irbesartan, torsemide)
  * Anticonvulsants (e.g., phenytoin)
  * Anticoagulants (e.g., warfarin)
  * Lipid lowering drugs (e.g., statins)

    * Caution should be taken when vemurafenib is co-administered with drugs that cause corrected QT interval (QTc) prolongation or cardiac arrhythmia, and when patients have a pre-existing cardiac disease or electrocardiogram (ECG) abnormality that may predispose them to cardiac dysrhythmia
    * Investigators should closely monitor patients who are on medications and/or supplements that may affect QT interval prolongation; such agents include, but are not limited to terfenadine, quinidine, procainamide, disopyramide, sotalol, probucol, bepridil, haloperidol, risperidone, indapamide and other drugs with dysrhythmic potential
* The subject 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 subject has radiographic evidence of cavitating pulmonary lesion(s)
* The subject has tumor in contact with, invading or encasing any major blood vessels
* The subject has evidence of tumor invading the gastrointestinal (GI) tract (esophagus, stomach, small or large bowel, rectum or anus), or any evidence of endotracheal or endobronchial tumor within 28 days before the first dose of cabozantinib
* The subject 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 or active treatment with drugs with dysrhythmic potential
    * 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: subjects 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

      * Intra-abdominal tumor/metastases invading GI mucosa
      * 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
    * 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 months 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 subject is unable to swallow tablets
* The subject has a corrected QT interval calculated by the Fridericia formula (QTcF) \> 500 ms within 28 days before randomization
* The subject is unable or unwilling to abide by the study protocol or cooperate fully with the investigator or designee
* For disease specific studies: the subject has had evidence within 2 years of the start of study treatment of another malignancy which required systemic treatment
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to XL184 or vemurafenib
* Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated on this study
* Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible