Bevacizumab With or Without TRC105 in Treating Patients With Metastatic Kidney Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed renal cancer; all histologic subtypes will be eligible * Patients must have metastatic disease which is measurable, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) to \>= 20 mm in the long axis by chest x-ray, \>= 10 mm in the long axis by spiral computed tomography (CT), magnetic resonance imaging (MRI), calipers, or clinical exam, or \>= 15 mm in the short axis for lymph nodes * Patients must have received at least 1 prior systemic therapy for renal cancer but no more than 4 prior therapies; they must have documented intolerance to or progression despite at least 1 systemic therapy; therapy administered in the adjuvant setting counts toward the prior systemic therapy total; if adjuvant therapy is the patient's only prior therapy the disease must have recurred during treatment or within 3 months of discontinuation * Allowable prior therapies include VEGF tyrosine kinase inhibitor (TKIs), mammalian target of rapamycin (mTOR) inhibitors, and cytokine therapy (example: interleukin-2 \[IL2\]) * At least 2 weeks must have elapsed from the last dose of the prior systemic therapy for biologics and 4 weeks for chemotherapy (6 weeks for nitrosoureas or mitomycin C); also note that at least 3 weeks should have elapsed since prior TKI administration * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Life expectancy of greater than 6 months * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin =\< institutional upper limits or normal (except for Gilbert's) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X institutional upper limit of normal (except subjects with liver metastases, who can have AST/ALT =\< 5 x ULN) * Creatinine glomerular filtration rate (GFR) (calculated or measured) \> 50 mL/min * Hemoglobin \>= 9 g/dL * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; 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; men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 6 months after completion of TRC105 or bevacizumab administration * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had systemic biologic therapy or radiotherapy within 2 weeks prior to entering the study or those who have not recovered from adverse events related to their prior therapy * Patients who have previously been treated with bevacizumab * Patients who have previously been treated with TRC105 * Patients who are receiving any other investigational agents * Known central nervous system (CNS) disease except for treated brain metastasis; 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 (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 CNS metastases treated by neurosurgical resection or brain biopsy performed within 3 months prior to day 1 will be excluded * History of allergic reactions attributed to compounds of similar chemical or biologic composition to TRC105 or bevacizumab * Patients on full-dose anticoagulation will be excluded; antiplatelet therapy will not be exclusionary * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, unhealed wound, gastrointestinal fistula, symptomatic congestive heart failure, unstable angina pectoris, myocardial infarction, cerebrovascular accident * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother wishes to participate in the study * Patients with a history of bleeding diathesis or inherited coagulopathy are excluded; in addition, those with a history of deep vein thrombosis (DVT) or pulmonary embolus within 1 year and still requiring active anticoagulation will be excluded; those with a more remote history of DVT or pulmonary embolus may be eligible but the risk of recurrent thrombosis should be considered * Patients with history of hereditary hemorrhagic telangiectasis (HHT-1 and HHT-2) * Serious or non-healing wound, ulcer, or bone fracture OR history of abdominal fistula, gastrointestinal perforation or intra-abdominal abscess within 6 months prior to day 1 * Invasive procedures defined as follows: * Major surgical procedure, open biopsy or significant traumatic injury within 28 days prior to day 1 therapy * Anticipation of need for major surgical procedures during the course of the study * Core biopsy within 7 days prior to day 1 therapy * Patients with clinically significant cardiovascular disease are excluded: * Inadequately controlled hypertension (HTN) (systolic blood pressure \[SBP\] \> 160 mmHg and/or diastolic blood pressure \[DBP\] \> 90 mmHg despite antihypertensive medication) * History of cerebrovascular accident (CVA) within 6 months * Myocardial infarction or unstable angina within 6 months * New York Heart Association grade II or greater congestive heart failure * Serious and inadequately controlled cardiac arrhythmia * Significant vascular disease (e.g. aortic aneurysm, history of aortic dissection) * Clinically significant peripheral vascular disease * Patients with known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies * Patients with psychiatric illness/social situations that would limit compliance with study requirements will be excluded