Brivanib Alaninate in Treating Patients With Persistent or Recurrent Cervical Cancer

Inclusion Criteria: * Patients must have persistent or recurrent squamous cell carcinoma, adenosquamous carcinoma, adenocarcinoma, or non-squamous cell carcinoma of the cervix with documented disease progression (disease not amenable to curative therapy); histologic confirmation of the original primary tumor is required via the pathology report * All patients must have measurable disease, defined by Response Evaluation Criteria In Solid Tumors (RECIST 1.1); measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded); each lesion must be \>= 10 mm when measured by computed tomography (CT), magnetic resonance imaging (MRI) or caliper measurement by clinical exam; or \>= 20 mm when measured by chest x-ray; lymph nodes must be \>= 15 mm in short axis when measured by CT or MRI * Patient must have at least one ?target lesion? to be used to assess response on this protocol as defined by RECIST 1.1 * Tumors within a previously irradiated field will be designated as ?non-target? lesions unless progression is documented or a biopsy is obtained to confirm persistence at least 90 days following completion of radiation therapy * Patients must not be eligible for a higher priority Gynecologic Oncology Group (GOG) protocol, if one exists * In general, this would refer to any active GOG phase III protocol or rare tumor protocol for the same patient population * Patients who have received one prior regimen must have a GOG performance status of 0, 1, or 2 * Patients who have received two prior regimens must have a GOG performance status of 0 or 1 * Recovery from effects of recent surgery, radiotherapy, or chemotherapy * Patients should be free of active infection requiring antibiotics (with the exception of uncomplicated urinary tract infection \[UTI\]) * Any hormonal therapy directed at the malignant tumor must be discontinued at least one week prior to registration * Any other prior therapy directed at the malignant tumor, including chemotherapy and immunologic agents, must be discontinued at least three weeks prior to registration * Any prior radiation therapy must be completed at least 4 weeks prior to registration * At least 4 weeks must have elapsed from the time of any major surgical procedure * Patients must have had one prior systemic chemotherapeutic regimen for management of advanced, metastatic, or recurrent carcinoma of the cervix; chemotherapy administered concurrent with primary radiation (e.g.; weekly cisplatin) is not counted as a systemic chemotherapy regimen for management of advanced, metastatic, or recurrent disease; adjuvant chemotherapy given following the completion of radiation therapy (or concurrent chemotherapy and radiation therapy) is not counted as a systemic chemotherapy regimen for management of advanced, metastatic, or recurrent disease (e.g.; paclitaxel and carboplatin for up to 4 cycles) * Patients are allowed to receive, but are not required to receive, one additional cytotoxic regimen for management of recurrent or persistent disease * Patients must have NOT received any non-cytotoxic (biologic or targeted) agents as part of their primary treatment or for management of recurrent or persistent disease * Non-cytotoxic (biologic or targeted) agents include (but are not limited to) monoclonal antibodies, cytokines, and small-molecule inhibitors of signal transduction * Absolute neutrophil count (ANC) greater than or equal to 1,500/mcl * Platelets greater than or equal to 100,000/mcl * Hemoglobin \>= 9 g/dl * Creatinine less than or equal to 1.5 x institutional upper limit of normal (ULN) * Urinalysis needs to be assessed at baseline and proteinuria must be less than or equal to 2+ by dipstick * If the urine dipstick is \> 2+, a 24-hour protein level can be done, as clinically indicated by the investigator * The 24-hour protein level must be less than or equal to 3.5 g/24 hours * Bilirubin less than or equal to 1.5 x ULN * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) less than or equal to 3 x ULN * Alkaline phosphatase less than or equal to 2.5 x ULN * Albumin greater than or equal to 2.5 g/dl * Neuropathy (sensory and motor) less than or equal to grade 1 * Prothrombin time (PT) such that international normalized ratio (INR) is =\< 1.5 x ULN; patients on therapeutic warfarin are excluded from trial, anticoagulation with low molecular weight heparin is allowed * Patients must have signed an approved informed consent and authorization permitting release of personal health information * Patients of childbearing potential must have a negative serum pregnancy test performed 48 hours prior to study entry and be practicing an effective form of contraception during the study and for at least 3 months after receiving the final treatment of brivanib * All patients must have a baseline electrocardiogram completed prior to study entry * Baseline electrocardiogram (ECG) should be repeated if corrected QT interval (QTc) is found to be \> 450 msec; QTc must NOT be \> 450 msec on both ECGs performed during the same visit Exclusion Criteria: * Patients who have had prior therapy with brivanib or anti-vascular, anti-PDGFR (platelet-derived growth factor receptor) or anti-FGFR (fibroblast growth factor receptor) therapy * Patients with a history of other invasive malignancies, with the exception of non-melanoma skin cancer and other specific malignancies, are excluded if there is any evidence of the other malignancy being present within the last three years; patients are also excluded if their previous cancer treatment contraindicates this protocol therapy * Patients who have received prior radiotherapy to any portion of the abdominal cavity or pelvis OTHER THAN for the treatment of cervical cancer within the last three years are excluded * Prior radiation for localized cancer of the breast, head and neck, or skin is permitted, provided that it was completed more than three years prior to registration, and the patient remains free of recurrent or metastatic disease * Patients who have received prior chemotherapy for any abdominal or pelvic tumor OTHER THAN for the treatment of cervical cancer within the last three years are excluded * Patients may have received prior adjuvant chemotherapy for localized breast cancer, provided that it was completed more than three years prior to registration, and that the patient remains free of recurrent or metastatic disease * Patients that are on required chronic anti-platelet therapy (aspirin \> 300 mg/day, or clopidogrel greater than or equal to 75 mg/day) * Patients with gastrointestinal bleeding or any other hemorrhage/bleeding event \>= grade 3 of the National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) within 30 days prior to study entry * Patients with a history of poor wound healing, non-healing ulcers, or bone fractures within the last 3 months * Patients with uncontrolled or significant cardiovascular disease including any of the following: * Myocardial infarction within 12 months * Uncontrolled angina within 12 months * Class III-IV New York Heart Association (NYHA) congestive heart failure * Uncontrolled hypertension despite anti-hypertensive therapy * Blood pressure (BP) must be less than or equal to 140/90 at screening * Subjects with a history of hypertension who are receiving treatment with calcium channel blockers that are cytochrome P450 family 3, subfamily A, polypeptide 4 (CYP3A4) inhibitors should be changed to an alternative antihypertensive medication before study entry * History of stroke, transient ischemic attack (TIA), or other central nervous system (CNS) ischemic event * Cardiac arrhythmias requiring anti-arrhythmic therapy other than beta blockers or digoxin * Patients must have pre-therapy left ventricular ejection fraction (LVEF) testing and have an ejection fraction \>= institutional lower limit of normal (LLN) * Patients with valvular heart disease \>= grade 2 * Patients with a serious uncontrolled medical disorder or active infection which would impair the ability of the subject to receive protocol therapy or whose control may be jeopardized by the complications of this therapy * Pre-existing thyroid abnormality with thyroid function that cannot be maintained in the normal range with medication * Patients with hyponatremia (sodium \< 130 mEq/L) * Patients with active/known human immunodeficiency virus (HIV), hepatitis B, or hepatitis C; HIV-positive subjects on combination antiretroviral therapy are ineligible * Patients with known brain metastases * Patients who are pregnant or nursing * Patients with inability to swallow tablets or untreated malabsorption syndrome * Patients with baseline serum potassium \< 3.5 mmol/L (potassium supplementation may be given to restore the serum potassium above this level prior to entry study) * Patients on therapeutic warfarin anticoagulation are excluded * Patients converted to anticoagulation with low molecular weight heparin will be allowed provided the patient?s PT is such that INR is =\< 1.5 x ULN