Sunitinib in Treating Patients With Recurrent and/or Metastatic Head and Neck Cancer

Criteria: * Hemoglobin \>= 9 g/dL * Histologically or cytologically confirmed squamous cell carcinoma of the head and neck: * Recurrent and/or metastatic disease * Measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 20 mm with conventional techniques OR as \>= 10 mm with spiral CT scan * No known brain metastases * Life expectancy \>= 2 months * ECOG performance status (PS) 0-1 or Karnofsky PS 70-100% (for patients in cohort A) * ECOG PS 2 or Karnofsky PS 60-70% (for patients in cohort B) * WBC \>= 3,000/mm\^3 * Absolute neutrophil count \>= 1,500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Calcium =\< 12.0 mg/dL * Bilirubin normal * AST and ALT =\< 2.5 times upper limit of normal * Creatinine normal OR creatinine clearance \>= 60 mL/min * QTc \< 500 msec * No New York Heart Association class III or IV heart failure: * Patients with the following are eligible provided they have New York Heart Association class II cardiac function on baseline ECHO/MUGA: * History of class II heart failure and asymptomatic on treatment * Prior anthracycline exposure * Prior central thoracic radiation that included the heart in the radiotherapy port * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No history of allergic reactions to compounds of similar chemical or biological composition to sunitinib malate * No history of serious ventricular arrhythmia (i.e., ventricular fibrillation or ventricular tachycardia \>= 3 beats in a row) * No history of other significant ECG abnormalities * No uncontrolled hypertension (defined as systolic blood pressure \[BP\] \>= 140 mm Hg or diastolic BP \>= 90 mm Hg) * No condition resulting in an inability to take oral medication, including any of the following: * Gastrointestinal tract disease resulting in an inability to take oral medication or a requirement for IV alimentation * Active peptic ulcer disease * No gastrostomy, jejunostomy, or other forms of enteral tube-feeding modalities * No serious or nonhealing wound, ulcer, or bone fracture * No abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within the past 28 days * No cerebrovascular accident or transient ischemic attack within the past 12 months * No myocardial infarction, cardiac arrhythmia, stable/unstable angina, symptomatic congestive heart failure, or coronary/peripheral artery bypass graft or stenting within the past 12 months * No pulmonary embolism within the past 12 months * No pre-existing uncontrolled thyroid abnormality (i.e., inability to maintain thyroid function within the normal range with medication) * No uncontrolled intercurrent illness, including either of the following: * Ongoing or active infection * Psychiatric illness or social situation that would limit compliance with study requirement * No more than two prior regimens for recurrent or metastatic disease: * Prior chemotherapy as part of initial curative intent therapy (e.g., neoadjuvant, adjuvant, or concurrent chemoradiotherapy) is allowed and will not count as prior therapy for recurrent or metastatic disease * At least 4 weeks since prior major surgery * At least 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin C) and recovered * At least 4 weeks since prior radiotherapy * No prior treatment with any other antiangiogenic agent (e.g., bevacizumab, sorafenib, pazopanib, AZD2171, vatalanib, or VEGF Trap) * No prior surgical procedure affecting absorption * At least 7 days since prior and no concurrent use of CYP3A4 inhibitors, including any of the following: * Azole antifungals (e.g., ketoconazole, itraconazole) * Verapamil * Clarithromycin * HIV protease inhibitors (e.g., indinavir, saquinavir, ritonavir, atazanavir, nelfinavir) * Erythromycin * Delavirdine * Diltiazem * At least 12 days since prior and no concurrent CYP3A4 inducers, including any of the following: * Rifampin * Phenytoin * Rifabutin * Hypericum perforatum (St. John's wort) * Carbamazepine * Efavirenz * Phenobarbital * Tipranavir * No concurrent therapeutic doses of coumarin-derivative anticoagulants (e.g., warfarin): Concurrent dosing of =\< 2 mg of warfarin daily for prophylaxis of thrombosis is allowed; Concurrent low molecular weight heparin allowed provided prothrombin time INR is =\< 1.5 * No other concurrent investigational agents * No concurrent agents with proarrhythmic potential, including any of the following: * Terfenadine * Quinidine * Procainamide * Disopyramide * Sotalol * Probucol * Bepridil * Haloperidol * Risperidone * Indapamide * Flecainide * No other concurrent anticancer agents or therapies * No concurrent combination antiretroviral therapy for HIV-positive patients