Sunitinib Malate in Treating Patients With Uterine Cervical Cancer That is Stage IVB, Recurrent, or Cannot Be Removed By Surgery

Inclusion Criteria: * Patients must have histologically or cytologically confirmed squamous cell carcinoma or adenosquamous carcinoma of the cervix; patients with adenocarcinoma of the cervix will also be included since, although infrequent, their management in general is similar to those with squamous tumors * Patients must have advanced (stage IVB) recurrent or persistent disease unsuitable for curative treatment by surgery and/or radiation therapy * Presence of clinically and/or radiologically documented disease; at least one site of disease must be unidimensionally measurable as follows: * X-ray, physical exam \>= 20 mm * Spiral computed tomography (CT) scan \>= 10 mm * Non-spiral CT scan \>= 20 mm * All radiology studies must be performed within 21 days prior to registration (within 28 days if negative) * Patients must have a life expectancy of at least 12 weeks * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1; performance status (PS) 2 patients are eligible if, in the opinion of the investigator, they are suitable for inclusion in the study and are likely to be compliant with the study procedures (in particular the recommendations for supportive care and dose modifications) * Patients may have had neoadjuvant or adjuvant chemotherapy * Patients may have had concurrent chemoradiation; this is not considered neoadjuvant or adjuvant treatment * Patients may have had no more than one prior chemotherapy regimen for recurrent metastatic disease; patients must be at least 28 days since last chemotherapy treatment and must have recovered from toxic effects * Patients may have had prior radiation therapy, including external beam and/or intracavity radiation; a minimum of 28 days must have elapsed between the end of radiotherapy and registration onto the study; patients must have recovered from any acute toxic effects from radiation prior to registration; radiation must have involved \< 30% of functioning bone marrow and there must be measurable disease outside the previously irradiated area (patients whose sole site of disease is in a previously irradiated area are ineligible UNLESS there is evidence of progression, or new lesions have been documented, in the irradiated field) * Previous major surgery is permitted provided that it has been at least 28 days prior to patient registration and that wound healing has occurred * Granulocytes (AGC) \>= 1.5 x 10\^9/L * Platelets \>= 100 x 10\^9/L * Bilirubin =\< upper limit of normal (ULN) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x ULN * Calcium =\< 3 mmol/L * Serum creatinine =\< ULN or creatinine clearance \>= 60ml/min if creatinine is \> ULN; creatinine clearance to be measured directly by 24 hour urine sampling or as calculated by Cockcroft Formula * Patient consent must be obtained according to local institutional and/or University Human Experimentation Committee requirements; it will be the responsibility of the local participating investigators to obtain the necessary local clearance, and to indicate in writing to the National Cancer Institute of Canada (NCIC) Clinical Trials Group (CTG) study coordinator that such clearance has been obtained, before the trial can commence in that center; because of differing requirements, a standard consent form for the trial will not be provided; a copy of the initial full board Research Ethics Board (REB) approval and approved consent form must be sent to the central office; the patient must sign the consent form prior to randomization or registration; please note that the consent form for this study must contain a statement which gives permission for the NCIC CTG and monitoring agencies to review patient records * Patients must be accessible for treatment, response assessment and follow-up; patients registered on this trial must be treated and followed at the participating center; this implies there must be reasonable geographical limits (for example: 1 ½ hour's driving distance) placed on patients being considered for this trial; investigators must assure themselves the patients registered on this trial will be available for complete documentation of the treatment, adverse events, and follow-up * In accordance with NCIC CTG policy, protocol treatment is to begin within 2 working days of patient registration; exceptions may be made however, regarding the washout period timing for prohibited medications Exclusion Criteria: * History of other malignancies, except: adequately treated non-melanoma skin cancer or other solid tumors curatively treated with no evidence of disease for \>= 5 years * Patients with known brain metastases; (a head CT is not necessary to rule out brain metastases, unless there is clinical suspicion of central nervous system \[CNS\] involvement); patients with known brain metastases will be excluded from this trial due to their poor prognosis and their likelihood of developing progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events * History of allergic reactions attributed to compounds of similar chemical or biologic composition to sunitinib * Patients receiving concurrent treatment with other anti-cancer therapy or other investigational anticancer agents * Patients who have received prior treatment with any other antiangiogenic agent or multi-targeted tyrosine kinase inhibitors (e.g., bevacizumab, sorafenib, pazopanib, thalidomide, AZD2171, AZD6474, AMG-706, PTK787, vascular endothelial growth factor \[VEGF\] Trap, etc.) are ineligible * Corrected QT (QTc) prolongation (defined as a QTc interval equal to or greater than 500 msec) or other significant electrocardiogram (ECG) abnormalities; an ECG must be done within 14 days prior to registration * Current or history of class III or IV heart failure as defined by the New York Heart Association (NYHA) functional classification system * Patients with prior anthracycline exposure, previous central thoracic radiation that included heart in radiation port, or a history of NYHA Class II cardiac function UNLESS * They are currently asymptomatic with respect to cardiac function AND * Left ventricular ejection fraction (LVEF) as assessed by multi gated acquisition (MUGA) at baseline is \> lower limit of normal (LLN) of institution; the MUGA must be done within 14 days prior to registration * Poorly controlled hypertension (systolic blood pressure of 140 mmHg or higher or diastolic blood pressure of 90 mmHg or higher) * 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 * History of pulmonary embolism within the past 12 months * History of cerebrovascular accident (CVA) or transient ischemic attack within 12 months prior to study entry * Patients who require use of therapeutic doses of Coumadin-derivative anticoagulants such as warfarin are excluded, although doses of up to 2 mg daily are permitted for prophylaxis of thrombosis; Note: low molecular weight heparin is permitted provided the patient's international normalized ratio (INR) is =\< 1.5; INR must be done within 7 days prior to registration * Patients with bowel obstruction or any condition (e.g. gastrointestinal tract disease resulting in an inability to take oral medication or a requirement for intravenous \[IV\] alimentation, prior surgical procedures affecting absorption, or active peptic ulcer disease) that impairs their ability to swallow and retain sunitinib tablets * Patients with serious illness or medical condition which would not permit the patient to be managed according to the protocol including, but not limited to: * History of significant neurologic or psychiatric disorder which would impair the ability to obtain consent or limit compliance with study requirements * Active uncontrolled infection * Any other medical conditions that might be aggravated by treatment * Serious or non-healing wound, ulcer, or bone fracture * Abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 28 days of treatment * Use of agents with proarrhythmic potential (terfenadine, quinidine, procainamide, disopyramide, sotalol, probucol, bepridil, haloperidol, risperidone, indapamide, and flecainide) is not permitted during the study * Patients receiving azole antifungals (ketoconazole, itraconazole), clarithromycin, erythromycin, diltiazem, verapamil, human immunodeficiency virus (HIV) protease inhibitors (indinavir, saquinavir, ritonavir, atazanavir, nelfinavir) and delavirdine are not eligible unless \>= 7 days since last dose before starting sunitinib and no dosing during the trial; patients receiving rifampin, rifabutin, carbamazepine, phenobarbital, phenytoin, St. John's wort, efavirenz and tipranavir are not eligible unless \>= 12 days since last dose before starting sunitinib and no dosing during the trial * Patients with pre-existing hypothyroidism prior to enrollment are ineligible unless they are euthyroid on medication * Some women enrolled on this study will have had a prior hysterectomy for cervical cancer * Pregnant or lactating women; (N.B.: All women of childbearing potential must have a negative urine beta- human chorionic gonadotropin (beta-HCG) pregnancy test within 7 days prior to registration) * Women of childbearing potential who do not 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 participating in this study, she should inform her treating physician immediately) * Known HIV-positive patients on combination antiretroviral therapy are ineligible