Everolimus With or Without Bevacizumab in Treating Patients With Advanced Kidney Cancer That Progressed After First-Line Therapy

Inclusion Criteria: * Renal cell carcinoma with some component of clear cell histology * Metastatic or unresectable disease * Must have been treated with at least 1 prior VEGFR tyrosine kinase inhibitor treatment and have progressed or have been intolerant to treatment * No prior systemic therapy with a vascular endothelial growth factor (VEGF) binding agent (e.g., bevacizumab) * No prior systemic therapy with any mechanistic target of rapamycin (mTOR) inhibitor (e.g., sirolimus, temsirolimus, everolimus) * Prior cytokine therapy is allowed * Any systemic therapy must be completed at least 4 weeks prior to registration * \>= 2 weeks since any prior radiation (including palliative) * Patients must not have had a major surgical procedure, open biopsy, or significant traumatic injury within 4 weeks prior to study registration, and must have fully recovered from any such procedure * The following are not considered to be major procedures: thoracentesis, paracentesis, port placement, laparoscopy, thoracoscopy, bronchoscopy, endoscopic ultrasonographic procedures, mediastinoscopy, skin biopsies, incisional biopsies and routine dental procedures * Patients must have measurable disease by RECIST criteria; lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 2 cm with conventional techniques or as \>= 1 cm with spiral computed tomography (CT) scan * No active brain metastases: patients with treated, stable brain metastases for at least three months are eligible as long as they meet the following criteria: * Treated brain metastases are defined as having no ongoing requirement for steroids and no evidence of progression or hemorrhage after treatment for at least 3 months, as ascertained by clinical examination and brain imaging (magnetic resonance imaging \[MRI\] or CT) (stable dose of anticonvulsants are allowed); treatment for brain metastases may include whole brain radiotherapy (WBRT), radiosurgery (RS; Gamma Knife, linear accelerator \[LINAC\], or equivalent) or a combination as deemed appropriate by the treating physician; patients with central nervous system (CNS) metastases treated by neurosurgical resection or brain biopsy performed within 3 months prior to day 1 are not eligible * Baseline brain imaging (MRI/CT) is required * No serious non-healing wound, ulcer, or bone fracture * No arterial thrombotic events within 6 months of registration: * Including transient ischemic attack (TIA), cerebrovascular accident (CVA), peripheral arterial thrombus, unstable angina or angina requiring surgical or medical intervention in the past 6 months, or myocardial infarction (MI); patients with clinically significant peripheral artery disease (i.e., claudication on less than one block), significant vascular disease (i.e., aortic aneurysm, history of aortic dissection), or any other arterial thrombotic event are ineligible * Patients who have experienced a deep venous thrombosis or pulmonary embolus within the past 6 months must be on stable therapeutic anticoagulation to be enrolled to this study * Patients receiving anti-platelet agents and prophylactic anticoagulation are eligible * No inadequately controlled hypertension: (defined as a blood pressure of \>= 160 mmHg systolic and/or \>= 90 mmHg diastolic on medication), or any prior history of hypertensive crisis or hypertensive encephalopathy * No known severe impairment of lung function, defined as \>= grade 2 dyspnea or cough, or either: * Requirement of supplemental oxygen, or * In cases where pulmonary function or pulse oximetry tests have been obtained, forced expiratory volume of the lung in one second (FEV1) or forced vital capacity (FVC) are \< 50% of predicted, or single breath diffusing capacity of the lung for carbon monoxide (DLCO) is \< 35% of predicted or resting room oxygen saturation is less than 90% * No active or severe liver disease (e.g. acute or chronic hepatitis, cirrhosis) * No positive serology for anti-hemoglobin C (HBC) or anti-hepatitis C virus (HCV) antibodies; hepatitis B virus (HBV) seropositive patients (hepatitis B surface antigen \[HBsAg\] positive) are eligible if they are closely monitored for evidence of active HBV infection by HBV deoxryribonucleic acid (DNA) testing and agree to receive suppressive therapy with lamivudine or other HBV-suppressive therapy until at least 4 weeks after the last dose of everolimus * No New York Heart Association (NYHA) class \>= 2 congestive heart failure * No active bleeding or chronic hemorrhagic diathesis or increased risk for bleeding: Including but not limited to history of major bleeding within 6 months (e.g. gastrointestinal, lung, CNS sites; or required transfusion support) * No history of abdominal fistula, gastrointestinal perforation or intra-abdominal abscess within 6 months prior to the initiation of treatment * No ongoing immunosuppressive therapy: including chronic systemic treatment with corticosteroids (\>= 10 mg/day prednisone equivalent) * Archival tissue must be available for submission: though it is optional patients to choose to participate in the correlative substudies or not * Patients who are pregnant or nursing are not eligible * Women of child bearing potential must have a negative serum or urine pregnancy test within 16 days prior to registration * Women of child-bearing potential include: * Any female who has experienced menarche and who has not undergone surgical sterilization (hysterectomy, bilateral tubal ligation or bilateral oophorectomy) or is not postmenopausal (defined as amenorrhea \>= 12 consecutive months) * Women on hormone replacement therapy (HRT) with documented serum follicle stimulating hormone (FSH) level \> 35m IU/mL * Women who are using oral, implanted or injectable contraceptive hormones or mechanical products such as an intrauterine device or barrier methods (diaphragm, condoms, spermicides) to prevent pregnancy or practicing abstinence or where partner is sterile (e.g., vasectomy) * Performance status Eastern Cooperative Oncology Group (ECOG) 0-2 or Karnofsky score \>= 60% * Granulocytes \>= 1,500/μL * Platelet count \>= 100,000/μL * Calculated creatinine clearance \>= 30 mL/minute (modified Cockroft and Gault formula) * Bilirubin =\< 1.5 x upper limits of normal * Aspartate aminotransferase (AST) =\< 2.5 x upper limits of normal (ULN) * Fasting serum triglycerides =\< 200 mg/dL * Serum cholesterol =\< 300 mg/dL * Fasting serum glucose =\< 1.5 x ULN * Urine protein to creatinine ratio \< 1.0 or urine protein =\< 1+