Sunitinib Malate and Hydroxychloroquine in Treating Patients With Advanced Solid Tumors That Have Not Responded to Chemotherapy

Inclusion Criteria: * Patients with histologically or cytologically proven advanced cancer * Patients must have undergone treatment with at least one regimen of standard therapy, either cytotoxic chemotherapy, an oral targeted agent or immunotherapy, or have a form of cancer for which no standard therapy exists, or are not eligible for or decline standard therapy; patients who have received prior therapy with sunitinib will be allowed; patients with prostate cancer may continue on hormonal therapy if they are currently receiving it * Patients must have measurable or evaluable disease according to Response Evaluation Criteria in Solid Tumors (RECIST) criteria * Life expectancy \> 12 weeks * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 9 g/dL * Serum calcium =\< 12.0 mg/dL * Total serum bilirubin within normal institutional limits * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/ananine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X institutional upper limit of normal, unless the patient has liver metastases, in which case both AST and ALT must be =\<5 X institutional upper limit of normal * Creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Thyroid-stimulating hormone (TSH) within normal institutional limits is required for eligibility; free T3 and free T4 values will also be obtained for baseline values should repeat parameters be required later in the course of treatment, however these values will not be used to determine eligibility * Creatine phosphokinase (CPK) within normal institutional limits * The following groups of patients are eligible provided they have New York Heart Association class II (NYHA) cardiac function on baseline echocardiogram (ECHO)/multi gated acquisition scan (MUGA): * Those with a history of class II heart failure who are asymptomatic on treatment * Those with prior anthracycline exposure * Those who have received central thoracic radiation that included the heart in the radiotherapy port * Patients who require use of therapeutic doses of Coumadin-derivative anticoagulants such as warfarin are excluded, although doses of up to 2 mg daily are permitted for prophylaxis of thrombosis; note: low molecular weight heparin is permitted provided the patient's prothrombin time (PT) international normalized ratio (INR) is =\< 1.5 * Ejection fraction measured within institutional limits of normal by MUGA scan * Patients with known brain metastases should be excluded because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events * 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 * Patients of childbearing or child fathering potential must be willing to use an acceptable method of birth control prior to study entry and for the duration of the study; acceptable methods of contraception include hormonal, barrier methods, intrauterine device, tubal ligation/vasectomy or abstinence; women should not breast feed while on treatment with sunitinib and HCQ * 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 * Patients with 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, or active peptic ulcer disease) that impairs their ability to swallow and retain sunitinib tablets are excluded * Approval for HCQ treatment by an eye doctor, based on a screening eye exam; examples of disqualifying baseline conditions include macular degeneration and other retinal disease, see exclusion criteria * Patients must be able to understand and sign informed consent Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy or biologic agents within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier; at least 4 weeks must have elapsed since any major surgery * Patients on treatment for rheumatoid arthritis or systemic lupus erythematosus * Patients receiving any disease-modifying anti-rheumatic drug (DMARD) * Active clinically significant infection requiring antibiotics, antivirals or antifungals; these medications may be allowed for instances of prophylaxis or treatment felt to not be clinically significant at the discretion of the principal investigator * Patients with poorly controlled hypertension (systolic blood pressure of 140 mmHg or higher or diastolic blood pressure of 90 mmHg or higher) are ineligible * Patients with a pre-existing thyroid abnormality who are unable to maintain thyroid function in the normal range with medication are ineligible * Diagnosis or history of central nervous system (CNS) disease (i.e. primary brain tumor, malignant seizures, untreated CNS metastases or carcinomatous meningitis or CNS metastases) * Patient must not have ongoing ventricular cardiac dysrhythmias of grade = 2 as described by the Cancer Therapy Evaluation Program (CTEP) Active Version of the National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE); patients with a history of serious ventricular arrhythmia (ventricular tachycardia \[VT\] or ventricular fibrillation \[VF\] \> 3 beats in a row) are also excluded; additionally, patients with ongoing atrial fibrillation are not eligible * Corrected QT (QTc) interval \>= 500 msec on baseline electrocardiogram (EKG) * Any of the following within 6 months prior to first dose of treatment: myocardial infarction, symptomatic coronary artery disease (severe or unstable angina), artery bypass graft, uncontrolled arrhythmias, symptomatic congestive heart failure, cerebrovascular accident or transient ischemic attack, or pulmonary embolus * Patients with known human immunodeficiency virus (HIV) are excluded due to possibility of unknown side effects on the immune system by these agents; the potential impact of pharmacokinetic interactions of retroviral therapy with sunitinib is unknown; appropriate studies may be undertaken in patients with HIV and those receiving combination anti-retroviral therapy in the future * Because sunitinib 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 * 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 must not have any known gastrointestinal (GI) pathology that would interfere with drug bioavailability * Patients must not have known prior hypersensitivity to sunitinib or hydroxychloroquine or any of their components * Must not be taking hydroxychloroquine for treatment or prophylaxis of malaria * Patients must not have a clinically significant bleeding or clotting disorder * Patients requiring medication with aurothioglucose (contraindicated with concurrent administration of antimalarials) * History of gastrointestinal perforation, or intra-abdominal abscess within the previous 28 days * Serious, non-healing infection, bone fracture or nonhealing ulcer or wound * Current treatment on another clinical trial; participation in non-therapeutic clinical trials is permissible * Patients with nephrotic syndrome * Cataracts that would interfere with required funduscopic examinations, or severe baseline visual impairment including macular degeneration, retinopathy or visual field changes, or having only one functional eye; all patients must undergo a screening eye exam prior to enrollment