Sorafenib in Treating Patients With Malignant Gastrointestinal Stromal Tumor That Progressed During or After Previous Treatment With Imatinib Mesylate and Sunitinib Malate

Inclusion Criteria: * Histologically confirmed gastrointestinal stromal tumor * Not amenable to curative surgery * Kit-expressing tumor * Disease progression (i.e., new lesion or 20% increase in unidimensional tumor size) on or after treatment with imatinib mesylate and sunitinib malate * Measurable disease, defined as ≥ 1 unidimensionally measurable lesion \> 20 mm by conventional techniques OR \> 10 mm by spiral CT scan * Only site of measurable disease must be outside of previously irradiated area * No known brain metastases * Performance status - ECOG 0-2 * More than 3 months * Absolute neutrophil count \> 1,500/mm\^3 * Platelet count \> 100,000/mm\^3 * Bilirubin normal * AST and ALT \< 2.5 times upper limit of normal * Creatinine ≤ 1.5 mg/dL * Creatinine clearance \> 60 mL/min * No symptomatic congestive heart failure * No unstable angina pectoris * No cardiac arrhythmia * No uncontrolled hypertension * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No other malignancy within the past 5 years except nonmelanoma skin cancer or carcinoma in situ of the cervix * No history of allergic reaction 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 uncontrolled illness * No evidence of bowel perforation or obstruction * No prior angiogenesis inhibitors * No immunotherapy after the last dose of imatinib mesylate or sunitinib malate * No chemotherapy or chemoembolization therapy after the last dose of imatinib mesylate or sunitinib malate * See Disease Characteristics * At least 4 weeks since prior radiotherapy and recovered * At least 14 days since prior imatinib mesylate or sunitinib malate * No prior sorafenib * No prior inhibitors of MAPK-signaling intermediates * No other investigational agent after the last dose of imatinib mesylate or sunitinib malate * Concurrent anticoagulation therapy with warfarin allowed provided the following criteria are met: * On a therapeutic stable warfarin dose * INR ≤3 * No active bleeding or pathologic condition that confers a high risk of bleeding * No concurrent combination antiretroviral therapy for HIV-positive patients * No concurrent administration of any of the following: * Enzyme-inducing antiepileptic drugs (e.g., carbamazepine, phenytoin, or phenobarbital) * Hypericum perforatum (St. John's wort) * Rifampin * No other concurrent anticancer agents or therapies