Sunitinib Malate and Bevacizumab in Treating Patients With Kidney Cancer or Advanced Solid Malignancies

Inclusion Criteria: * Patients must have histologically or cytologically confirmed renal cell; or other solid malignancy (excluding lymphoma) that is metastatic or unresectable and for which no standard curative therapy exists; for the renal cell cancer subset, a component of clear cell histology is required (a minimum of 6 subjects with clear cell kidney cancer will be enrolled per treatment stratification; additional subjects enrolled per imaging cohort will allow "other" solid tumors) * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 20 mm with conventional techniques or as \>= 2 times the slice width with spiral CT scan (i.e. 10 mm if the CT slice width is 5 mm, 14 mm if the CT slice width is 7 mm) * Life expectancy of greater than 12 weeks * 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 \[SGOT\]))/alanine aminotransferase (ALT)(serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal, unless subjects have liver metastases, in which case both AST and ALT must be =\< 5 × institutional upper limit of normal * Creatinine =\< 1.5 x normal institutional limits OR * Creatinine clearance (measured) \>= 50 mL/min/1.73m\^2 for patients with creatinine levels above 1.5 x normal institutional limits * Urine protein should be screened by urine analysis for urine protein creatinine (UPC) ratio; for a UPC ratio \> 0.5, a 24-hour urine protein should be obtained and the level should be \< 1,000 mg for eligibility; Note: UPC ratio of spot urine is an estimation of the 24 hour urine protein excretion; A UPC ratio of 1 is roughly equivalent to a 24-hour urine protein of 1 gram; UPC ratio is calculated by the following formula: * \[urine protein\]/\[urine creatinine\] (if both urine protein and creatinine reported as mg/dL) * \[(urine protein) x 0.088\]/\[urine creatinine\] (if urine creatinine is reported in mmol/L) * All patients being evaluated for the imaging cohort need to be willing to undergo planned pharmacodynamic assessments, including serial PET imaging, plasma markers, and pharmacokinetic sampling * Women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for at least 6 months after the completion of bevacizumab therapy; all women of childbearing potential must have a negative pregnancy test prior to receiving sunitinib; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Breastfeeding is not allowed while on study and for the duration of study participation; the duration of such precautions after discontinuation of bevacizumab should take into consideration the half-life of bevacizumab (average 21 days, range 11-50 days) * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy, radiotherapy, experimental therapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered (to grade =\< 1 or baseline) from clinically significant adverse events due to agents administered more than 4 weeks earlier (alopecia excluded); clinical significance to be determined by investigator * Patients may not be receiving any other investigational agents * Patients who have received prior treatment with any other VEGF signaling pathway inhibitors (e.g., bevacizumab, sorafenib, pazopanib, AZD2171, PTK787, VEGF Trap, etc.) are ineligible * History of allergic reactions attributed to compounds of similar chemical or biologic composition to sunitinib or bevacizumab * Patients with QTc prolongation (defined as a QTc interval greater than or equal to 500 msec) or other significant electrocardiogram (ECG) abnormalities (per investigator discretion) are excluded * Patients who require use of therapeutic doses of Coumarin-derivative anticoagulants such as warfarin are excluded, although doses of up to 2 mg daily are permitted for prophylaxis of thrombosis; Note: full-dose low-molecular weight heparin (or other blood thinners) will be excluded as well given potential for bleeding with this regimen; prophylactic doses of low-molecular weight heparin (LMWH) will be allowed if prothrombin time (PT)/international normalized ratio (INR) is =\< 1.5 * Patients with any condition (e.g., gastrointestinal tract disease resulting in an inability to take oral medication or a requirement for IV alimentation, prior surgical procedures affecting absorption, or active peptic ulcer disease) that impairs their ability to swallow and retain sunitinib tablets are excluded * Patients must have blood pressure (BP) no greater than 140 mmHg (systolic) and 90 mmHg (diastolic) for eligibility; initiation or adjustment of BP medication is permitted prior to study entry provided that the average of three BP readings at a visit prior to enrollment is less than 140/90 mmHg * Patients with clinically significant cardiovascular disease are excluded * Any history of cerebrovascular accident (CVA) or transient ischemic attack within 12 months prior to study entry * History of myocardial infarction, cardiac arrhythmia, stable/unstable angina, symptomatic congestive heart failure, or coronary/peripheral artery bypass graft or stenting within 12 months prior to study entry * Serious and inadequately controlled cardiac arrhythmia * Significant vascular disease (e.g. aortic aneurysm, history of aortic dissection) * Clinically significant peripheral vascular disease * History of pulmonary embolism within the past 12 months * Class III or IV heart failure as defined by the New York Heart Association (NYHA) functional classification system * Patients with any of the following conditions are excluded: * Serious or non-healing wound, ulcer, or bone fracture * History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 6 months prior to day 1 * Because sunitinib is metabolized primarily by the cytochrome P450 3A4 (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 change medication regimens to include only those that do not affect CYP3A4, particularly patients who are taking enzyme-inducing anticonvulsant agents; any identified agent must be stopped at least 2 weeks prior to study registration * Use of agents with proarrhythmic potential (including but not limited to: terfenadine, quinidine, procainamide, disopyramide, sotalol, probucol, bepridil, haloperidol, risperidone, indapamide, and flecainide) are not permitted during the study; a comprehensive list of agents with proarrhythmic potential can be found at http://azcert.org * Steroid use is not recommended during sunitinib treatment unless absolutely necessary (e.g., for treatment of adverse events or protocol-required premedication) because many steroids (e.g., prednisone, prednisolone, dexamethasone, etc.) effectively lower sunitinib exposure through CYP3A4 interactions; patients currently using steroids must be discussed with investigator prior to enrollment * Patients with a pre-existing thyroid abnormality who are unable to maintain thyroid function in the normal range with medication are ineligible; patients with a history of hypothyroidism are eligible provided they are currently euthyroid * 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 * Patients with uncontrolled intercurrent illness including, but not limited to, ongoing or active infections or psychiatric illness/social situations that would limit compliance with study requirements are ineligible * Pregnant (positive pregnancy test) women are excluded from this study; breastfeeding should be discontinued if the mother is treated with sunitinib malate * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible; appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated * Evidence of a bleeding diathesis or coagulopathy * Invasive procedures defined as follows: * Major surgical procedure, open biopsy or significant traumatic injury within 28 days prior to day 1 therapy * Core biopsy within 7 days prior to day 1 therapy * It is also appropriate to exclude subjects for whom there is the reasonable possibility that they will require major surgical procedures during the trial * Patients with known hypersensitivity of Chinese hamster ovary cell products or other recombinant human antibodies * For subjects with lung cancer, the following exclusions apply: * Lung carcinoma of squamous cell histology (mixed tumors will be categorized by the predominant cell type unless small cell elements are present, in which case the patient is ineligible; sputum cytology alone is not acceptable) * History of hemoptysis (bright red blood of 1/2 teaspoon or more per episode) within 3 months prior to study enrollment * Current, ongoing treatment with full-dose warfarin or its equivalent (i.e., unfractionated and/or low molecular weight heparin) * Current or recent (within 10 days of enrollment) use of aspirin (\>325 mg/day) or chronic use of other nonsteroidal anti-inflammatory drugs (NSAIDs) * Subjects with a history of thrombotic microangiopathy are excluded