Sorafenib in Treating Patients With Advanced Anaplastic Thyroid Cancer

Criteria: * Progressive disease after prior cytotoxic chemotherapy (i.e., chemotherapy alone or combined with radiotherapy) * No symptomatic bulky disease that would impair the airway or impede swallowing (for patients with ECOG performance status 2) * No known brain metastases * Measurable or evaluable disease * Measurable disease, defined as ≥ 1 unidimensionally measurable lesion \>= 20 mm by conventional techniques OR \>= 10 mm by spiral CT scan * Measurable disease not in a previously irradiated field * Patients with evidence of abnormal cardiac conduction (e.g., bundle branch block or heart block) are eligible provided disease has been stable for the past 6 months * Performance status: * ECOG 0-2 OR Karnofsky 50-100% * Life expectancy more than 8 weeks * Absolute neutrophil count \>= 1,250/mm3 * Platelet count \>= 100,000/mm3 * No evidence of bleeding diathesis * Bilirubin =\< 1.5 times upper limit of normal (ULN) * PTT =\< 1.5 times ULN * Creatinine =\< 1.5 times ULN * No myocardial infarction within the past 6 months * No New York Heart Association class III or IV cardiac disease * No symptomatic congestive heart failure * No unstable angina pectoris * No uncontrolled hypertension (i.e., systolic blood pressure (BP) \> 150 mm Hg OR diastolic BP \> 100 mm Hg) * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * Able to swallow oral medication * No history of allergic reactions attributed to compounds of similar chemical or biological composition to sorafenib * No ongoing or active infection * No psychiatric illness or social situation that would preclude study compliance * No other invasive malignancy within the past 5 years except nonmelanoma skin cancer * No other uncontrolled illness * No more than 2 prior systemic cytotoxic chemotherapy regimens (combined modality systemic cytoxic chemotherapy is considered 1 prior cytotoxic regimen) * At least 7 days since prior chemotherapy and recovered * At least 7 days since prior radiotherapy and recovered * No prior sorafenib or other inhibitors of MAP kinase signaling intermediates * No prior cancer treatment that would preclude study participation * No concurrent combination antiretroviral therapy for HIV-positive patients * No other concurrent investigational agents * No concurrent cytochrome P450 enzyme-inducing antiepileptic drugs (e.g., phenytoin, carbamazepine, or phenobarbital) * No concurrent Hypericum perforatum (St. John's wort) or rifampin * No concurrent therapeutic anticoagulation (concurrent prophylactic anticoagulation (i.e., low-dose warfarin) for venous or arterial access devices allowed provided requirements for INR and PTT are met) * No other concurrent anticancer therapy * Histologically confirmed anaplastic\* thyroid cancer * Not amenable to definitive curative surgery or radiotherapy \[Note: \*Papillary, follicular, or other histologies that are mixed or identified in a diagnostic tissue sample are allowed provided a high-grade undifferentiated anaplastic component is present \] * No cardiac arrhythmia * AST and ALT =\< 3.5 times ULN * INR \< 2.0