Akt Inhibitor MK2206 and Hydroxychloroquine in Treating Patients With Advanced Solid Tumors, Melanoma, Prostate or Kidney Cancer

Inclusion Criteria:

* Patients with histologically or cytologically proven advanced solid cancer and have undergone treatment with at least one regimen of standard therapy, either cytotoxic chemotherapy, a molecularly targeted agent, or immunotherapy, or have a form of cancer for which no standard therapy exists; patients with prostate cancer may continue on androgen-deprivation therapy if they are currently receiving it
* Patient must have recovered from toxicity of prior chemotherapy, molecularly targeted agents and/or radiotherapy; patient may not have received chemotherapy in the prior 4 weeks (6 weeks for nitrosoureas or mitomycin C); patients may have not received a molecularly targeted agent within the past 4 weeks or 5 half lives (whichever is less); patients may not have received radiotherapy in the prior 3 weeks
* Patients must be willing and able to sign informed consent
* Leukocytes \>= 3,000/mcL (obtained within 7 days of treatment initiation)
* Absolute neutrophil count \>= 1,500/mcL (obtained within 7 days of treatment initiation)
* Platelets \>= 100,000/mcL (obtained within 7 days of treatment initiation)
* Total serum bilirubin within normal institutional limits (obtained within 7 days of treatment initiation)
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X institutional upper limit of normal (obtained within 7 days of treatment initiation)
* Creatinine =\< grade 1 OR creatinine clearance \>= 40 mL/min/1.73 m\^2 for patients with creatinine (Cr) above normal institutional limits; a calculated creatinine clearance by Cockcroft-Gault Formula is acceptable in lieu of a measured value (obtained within 7 days of treatment initiation)
* All patients must have measurable or evaluable disease per Response Evaluation Criteria in Solid Tumors (RECIST) criteria
* Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status =\< 1
* Estimated life expectancy of at least 12 weeks
* Women must: have a negative serum or urine pregnancy test within 7 days prior to study entry if she is a woman of child-bearing potential (WOCBP), or be at least one year post-menopausal, OR be surgically sterile
* The effects of MK-2206 on the developing human fetus are unknown; for this reason, women of child-bearing potential and men must agree to use adequate contraception prior to study entry, for the duration of study participation and for 6 months after study participation; acceptable methods of contraception include hormonal, barrier methods, intrauterine device, tubal ligation/vasectomy or abstinence; 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; acceptable methods of contraception include hormonal, barrier methods, intrauterine device, tubal ligation/vasectomy or abstinence; women should not breast feed while on treatment with MK-2206 and hydroxychloroquine
* Patients must not have a history of any condition (social or medical) that, in the opinion of the investigator, might interfere with the patient's ability to comply with the protocol or pose additional or unacceptable risk to the patient
* Approval for hydroxychloroquine treatment by an eye doctor, based on a screening eye exam; examples of disqualifying baseline conditions may include macular degeneration and other retinal disease such as cataracts that would interfere with required funduscopic examinations, or severe baseline visual impairment, retinopathy or visual field changes; all patients must undergo a screening eye exam prior to enrollment
* Patients must be able to swallow whole tablets; nasogastric or gastrostomy (G) tube administration is not allowed; tablets must not be crushed or chewed

Exclusion Criteria:

* Failure to recover fully (as judged by the investigator) from prior surgical procedures, or failure to recover from adverse events (grade =\< 1) due to agents administered more than 4 weeks earlier
* Concurrent treatment with an investigational agent other than the investigational agent(s) used in this study OR treatment within 4 weeks of study entry with any investigational agent(s) or device(s)
* Patients with corrected QT interval (QTc) prolongation greater than Common Terminology Criteria for Adverse Events (CTCAE) grade 1 (\> 480 msec); in addition, patients should not be receiving non-study medications known to prolong QTc
* Patients on treatment for rheumatoid arthritis or systemic lupus erythematosus
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to agents used in study
* Patient has uncontrolled diabetes, defined as a fasting serum glucose \> 150 mg/dl or glycosylated hemoglobin (hemoglobin A1c \[HbA1c\]) \> 7% at screening
* Diabetic patients requiring insulin for glucose control at the time of study entry
* Patient must not have ongoing ventricular cardiac dysrhythmias of grade \>= 2 as described by the Cancer Therapy Evaluation Program (CTEP) version 4.0 of the National Cancer Institute (NCI) CTCAE
* Any condition (e.g., gastrointestinal tract disease resulting in an inability to take oral medication or a requirement for intravenous \[IV\] alimentation, prior surgical procedures affecting absorption, ulcerative colitis, inflammatory bowel disease, a partial or complete small bowel obstruction, or active peptic ulcer disease) that impairs their ability to swallow and retain MK-2206 or hydroxychloroquine tablets
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, or psychiatric illness/social situations that would affect safety or limit compliance with study requirements
* Pregnant and nursing women are excluded from this study because developmental and reproductive toxicity studies of MK-2206 have not been performed
* Known human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with MK-2206 or HCQ used in this study
* Because MK-2206 is metabolized primarily by the cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) liver enzyme, the eligibility of patients taking medications that are potent inducers or inhibitors of that enzyme will be determined following a review of their case by the principal investigator; every effort should be made to switch patients taking such agents or substances to other medications
* Patients with active central nervous system (CNS) metastases are excluded; patients with CNS metastases that have been treated must be off steroid treatment for \> 2 months and be asymptomatic; patients that have symptoms to suggest CNS metastases should have a brain magnetic resonance imaging (MRI) within 28 days of enrollment to confirm the absence of CNS metastases; contrast computed tomography (CT) is acceptable for patients who are unable to undergo a brain MRI
* Must not have psoriasis or porphyria
* Must not have known hypersensitivity to 4-aminoquinoline compound
* Must not have retinal or visual field changes from prior 4-aminoquinoline compound use
* Must not have known glucose-6-phosphate dehydrogenase (G-6PD) deficiency
* Patients with liver disease such as cirrhosis, chronic active hepatitis, or chronic persistent hepatitis
* Must not be taking hydroxychloroquine for treatment or prophylaxis of malaria
* Current treatment on another clinical trial; participation in non-therapeutic clinical trials is permissible