Sunitinib in Treating Patients With Advanced Malignant Pleural Mesothelioma

Criteria: * Histologically or cytologically confirmed malignant pleural mesothelioma; Advanced or metastatic disease incurable by standard therapies * Measurable disease, defined as at least 1 unidimensionally measurable lesion \>= 20 mm by conventional techniques or \>= 10 mm by spiral CT scan; No sole site of disease in a previously irradiated area unless there has been subsequent evidence of progression; Low-dose, palliative radiotherapy allowed * Meets 1 of the following criteria for prior cytotoxic chemotherapy treatment: Previously treated with 1 platinum-based chemotherapy regimen; Previously untreated (i.e., no prior cytotoxic chemotherapy) * No known brain metastases * ECOG performance status 0-1 * Life expectancy \>= 12 weeks * Platelet count \>= 100,000/mm\^3 * Absolute granulocyte count \>= 1,500/mm\^3 * Bilirubin normal * AST and ALT =\< 2.5 times upper limit of normal * Calcium =\< 3 mmol/L * Creatinine normal OR creatinine clearance \>= 60 mL/min * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * Patients must reside within a 1.5 hour drive from participating center * Able to take oral medication * No other malignancy within the past 5 years except adequately treated nonmelanoma skin cancer, curatively treated in-situ carcinoma of the cervix, or any other curatively treated solid tumor * No known history of allergic reactions attributed to compounds of similar chemical or biologic composition to sunitinib malate * No QTc prolongation (i.e., QTc interval \>= 500 msec) or other significant ECG abnormalities * No New York Heart Association (NYHA) class III or IV heart failure * Patients with the following histories allowed provided they are asymptomatic with respect to cardiac function and LVEF is normal by MUGA at baseline: Anthracycline exposure, Central thoracic radiation that included the heart, NYHA class II cardiac function * No uncontrolled hypertension (i.e., systolic blood pressure \>= 140 mm Hg or diastolic blood pressure \>= 90 mm Hg) * No cardiac disease within the past 12 months, including any of the following: myocardial infarction, cardiac arrhythmia, stable/unstable angina, symptomatic congestive heart failure * No pulmonary embolism within the past 12 months * No cerebrovascular accident or transient ischemic attack within the past 12 months * No bowel obstruction or any condition that would impair the ability to swallow and retain sunitinib malate, including any of the following: gastrointestinal tract disease resulting in an inability to take oral medication, requirement for IV alimentation, active peptic ulcer disease * No serious illness or medical condition that would preclude study treatment including, but not limited to, any of the following: history of significant neurologic or psychiatric disorder that would impair the ability to obtain consent or limit compliance with study requirements, Active uncontrolled infection, Any other medical condition that might be aggravated by treatment, OR; * Serious or nonhealing wound, ulcer, or bone fracture, Abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within the past 28 days * No pre-existing hypothyroidism unless euthyroid on medication * At least 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin C) and recovered * At least 7 days since prior and no concurrent CYP3A4 inhibitors, including any of the following: Azole antifungals (e.g., ketoconazole, itraconazole, miconazole), Verapamil, Clarithromycin, HIV protease inhibitors (e.g., indinavir, saquinavir, ritonavir, atazanavir, or nelfinavir) Erythromycin, Delavirdine, Diltiazem * At least 12 days since prior and no concurrent CYP3A4 inducers, including any of the following: Rifampin, Phenytoin, Rifabutin, Hypericum perforatum (St. John's wort), Carbamazepine, Efavirenz Phenobarbital, Tipranavir * At least 4 weeks since prior major surgery and recovered * At least 4 weeks since prior radiotherapy and recovered * At least 12 months since prior coronary/peripheral artery bypass graft or stenting * No prior surgical procedures affecting absorption * No prior radiotherapy that involved \>= 30% of functioning bone marrow * No prior treatment with any other antiangiogenic agents or multitargeted tyrosine kinase inhibitors, including any of the following: bevacizumab, sorafenib tosylate, pazopanib, thalidomide, AZD2171, vandetanib, AMG706, vatalanib, VEGF Trap * No prior angiogenesis inhibitors except epidermal growth factor receptor inhibitors or other noncytotoxic therapy * No other concurrent anticancer therapy or treatment with other investigational anticancer agents * No concurrent combination antiretroviral therapy for HIV-positive patients * No concurrent therapeutic doses of coumadin-derivative anticoagulants (e.g., warfarin); Doses =\< 2 mg/day for prophylaxis of thrombosis or low molecular weight heparin for patients with an INR \< 1.5 are allowed * No concurrent agents with proarrhythmic potential, including any of the following: terfenadine, quinidine, procainamide, disopyramide, sotalol, probucol, bepridil, haloperidol, risperidone, indapamide, flecainide