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 imm…