Bevacizumab With or Without Trebananib in Treating Patients With Recurrent Brain Tumors

Inclusion Criteria:

* Histologically proven diagnosis of glioblastoma or variants (gliosarcoma, glioblastoma with oligodendroglial features, giant cell glioblastoma); patients will be eligible if the original histology was a lower grade glioma and a subsequent histological diagnosis of glioblastoma or variants is made
* The tumor must be supratentorial; patients with infratentorial disease, spinal cord disease, and/or leptomeningeal disease are excluded
* Patients must have shown unequivocal evidence for tumor progression on the previous treatment regimen (prior to enrollment on this study) by magnetic resonance imaging (MRI) scan of the brain with and without contrast within 14 days prior to registration; the dose of steroids must be stable or decreasing for at least 5 days prior to the scan; patients with tumor progression who then undergo surgical resection prior to enrollment on study may be eligible as long as pathology confirms progressive or recurrent glioblastoma multiforme (GBM) (or variants); for patients who undergo surgical resection, registration on study may not occur any sooner than 28 days from surgery; an MRI scan of the brain with and without contrast is still required within 14 days prior to registration on study but is not required to demonstrate measurable disease or tumor progression after surgery
* Patients unable to undergo MRI because of non-compatible devices can be enrolled, provided computed tomography (CT) scans are obtained and are of sufficient quality; patients without non-compatible devices may not have CT scans performed to meet this requirement
* History/physical examination within 14 days prior to registration
* Karnofsky performance scale \>= 70 within 14 days prior to registration
* Patients who have received prior treatment with interstitial brachytherapy, stereotactic radiosurgery, or implanted chemotherapy sources, such as wafers of polifeprosan 20 with carmustine, must have confirmation of progressive disease within 14 days prior to registration based upon nuclear imaging, magnetic resonance (MR) spectroscopy, perfusion imaging, or histopathology
* Leukocytes \> 3,000/mm\^3 (within 14 days prior to registration)
* Absolute neutrophil count (ANC) \>= 1,500 cells/mm\^3 (within 14 days prior to registration)
* Hemoglobin \>= 10.0 g/dL (note: the use of transfusion or other intervention to achieve hemoglobin \[Hgb\] \>= 10.0 g/dL is acceptable) (within 14 days prior to registration)
* Platelets \>= 100,000 cells/mm\^3 (within 14 days prior to registration)
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) \< 2.5 X institutional upper limit of normal (within 14 days prior to registration)
* Bilirubin =\< 2.0 mg/dL (within 14 days prior to registration)
* Creatinine within normal upper institutional limits or creatinine clearance \> 60 mL/min/1.73 m\^2 (per 24 hour urine collection or calculated according to the Cockcroft-Gault formula) for subjects with creatinine levels above the institutional normal (within 14 days prior to registration)

  * Patients with creatinine levels below normal institutional limits are eligible
* Prothrombin time (PT)/international normalized ratio (INR) =\< 1.5 (within 14 days prior to registration)
* Urinary protein =\< 30 mg/dL in urinalysis or =\< 1+ on dipstick (within 14 days prior to registration)
* Generally well-controlled blood pressure with systolic blood pressure =\< 140 mm Hg AND diastolic blood pressure =\< 90 mm Hg within 5 days prior to registration; the use of anti-hypertensive medications to control hypertension is permitted
* Women of childbearing potential must have a negative serum beta-human chorionic gonadotropin (HCG) pregnancy test within 14 days prior to registration
* Women of childbearing potential and male patients who are sexually active must practice adequate contraception during therapy and for 180 days (6 months) afterwards
* Patient must provide study specific informed consent prior to study entry

Exclusion Criteria:

* Prior invasive malignancy (except non-melanomatous skin cancer) unless disease free for a minimum of 3 years (for example, carcinoma in situ of the breast, oral cavity, or cervix are all permissible)
* Prior systemic cytotoxic chemotherapy within (i.e., =\<) 28 days (42 days for nitrosoureas or mitomycin C) prior to registration, or patients who have not returned to baseline or =\< Common Terminology Criteria for Adverse Events (CTCAE) version 4 (v. 4) grade 2 from adverse events (excluding alopecia) due to agents administered more than 28 days prior to registration
* Patients who received non-cytotoxic drug therapy must be off treatment for at least 14 days prior to registration; prior treatment with anti-vascular endothelial growth factor (VEGF) targeted agents; AMG 386 therapy; or other molecules that inhibit angiopoietins or TEK tyrosine kinase, endothelial (Tie2) receptor including, but not limited to, XL-820, XL-184 (cabozantinib-s-malate), and CVX-060/PF-4856884 is not allowed regardless of time frame
* Patients who have not yet completed at least 21 days (30 days for prior monoclonal antibody therapy) since ending other investigational device or drug trials, or who are currently receiving other investigational treatments
* Treatment within 30 days prior to enrollment with strong immune modulators, including but not limited to systemic cyclosporine, tacrolimus, sirolimus, mycophenolate mofetil, methotrexate, azathioprine, rapamycin, thalidomide, lenalidomide, and targeted immune modulators such as abatacept (CTLA-4-Ig), adalimumab, alefacept, anakinra, belatacept (LEA29Y), efalizumab, etanercept, infliximab, or rituximab
* Prior radiotherapy within 90 days (3 months) prior to registration unless there is either: a) histopathologic confirmation of recurrent tumor; or b) new enhancement on MRI outside of the radiation treatment field
* Major surgical procedure (including craniotomy and open brain biopsy) or significant traumatic injury within 28 days prior to registration or those patients who receive a non-central nervous system (CNS) minor surgical procedures (e.g. core biopsy or fine needle aspiration) within 3 days prior to registration; there is no waiting period for central line placement; there is a 7-day window for recovery prior to registration for patients who underwent stereotactic biopsy of the brain
* Prior therapy with anti-VEGF targeted agents (e.g. bevacizumab, cediranib, vandetanib, aflibercept, sunitinib, sorafenib, etc.); prior therapy with thalidomide and lenalidomide is allowed as long as treatment has not occurred within 30 days prior to enrollment
* More than 2 relapses
* Therapeutic anticoagulation with warfarin \< 7 days prior to registration; (therapeutic or prophylactic therapy with aspirin, a low-molecular weight heparin, or a Factor Xa inhibitor is acceptable)
* Intratumoral hemorrhage or peritumoral hemorrhage, demonstrated by MRI or CT scan, CTCAE, v. 4 grade 2 or greater or evidence of significant hemorrhage (regardless of CTCAE, v. 4 grade) defined as \> 1 cm diameter of blood (including postoperative hemorrhage)
* Gastrointestinal bleeding or any other hemorrhage/bleeding event CTCAE, v. 4 grade 3 or greater within 30 days prior to study entry
* Severe, active co-morbidity, defined as follows:

  * Unstable angina and/or congestive heart failure requiring hospitalization within 180 days (6 months) prior to registration
  * Transmural myocardial infarction within 180 days (6 months) prior to registration
  * History of stroke, cerebral vascular accident (CVA), or transient ischemic attack within 180 days (6 months) prior to registration
  * Acute bacterial or fungal infection requiring intravenous antibiotics at the time of registration
  * Chronic obstructive pulmonary disease exacerbation or other respiratory illness requiring hospitalization or precluding study therapy at the time of registration
  * Hepatic insufficiency resulting in clinical jaundice and/or coagulation defects
  * Acquired immune deficiency syndrome (AIDS) based upon current Centers for Disease Control and Prevention (CDC) definition; note, however, that human immunodeficiency virus (HIV) testing is not required for entry into this protocol
  * Known coagulopathy that increases risk of bleeding or a history of clinically significant hemorrhages in the past
  * History of non-healing wounds or ulcers, or bone fractures within 90 days (3 months) prior to registration
  * History of venous or arterial thromboembolism within 12 months prior to registration
* Prior allergic reaction to the study drugs involved in this study