Sorafenib and Isolated Limb Infusion of Melphalan in Treating Patients With Stage III Melanoma of the Arm or Leg

DISEASE CHARACTERISTICS: * Histologically confirmed primary or recurrent extremity melanoma * Stage IIIB or IIIC disease * Patients with stage IIIC disease must have had regional lymph nodes previously removed * Disease to be treated by regional therapy must be distal to the planned site of tourniquet placement * Bidimensionally measurable disease by caliper or radiological method * Must have identifiable target lesions for disease assessment * Patients with a single lesion must have archived tumor tissue available for research analysis * No stage IV disease * No known brain metastasis * Patients with neurological symptoms must have undergone a CT scan or MRI of the brain within the past 4 weeks to exclude brain metastasis PATIENT CHARACTERISTICS: * ECOG or Zubrod performance status 0-1 * Life expectancy \> 6 months * Hemoglobin ≥ 9.0 g/dL * WBC ≥ 3,000/mm\^3 * ANC ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 * Total bilirubin ≤ 1.5 x upper limit of normal (ULN) * ALT and AST ≤ 2.5 x ULN * INR \< 1.5 or PT/PTT normal * Creatinine ≤ 1.5 x ULN * Not pregnant or nursing * Negative serum pregnancy test * Fertile patients must use effective contraception * Must have a palpable femoral or axillary pulse in the extremity to be treated * No cardiac disease, including any of the following: * NYHA class III or IV congestive heart failure * Unstable angina (i.e., angina symptoms at rest) or new onset angina within the past 3 months * Myocardial infarction within the past 6 months * No cardiac ventricular arrhythmias requiring antiarrhythmic therapy * No uncontrolled hypertension, defined as systolic blood pressure (BP) \> 150 mm Hg or diastolic BP \> 90 mm Hg, despite optimal medical management * No known HIV infection * No chronic hepatitis B or C * No active clinically serious infection \> CTCAE grade 2 * No thrombotic or embolic events (e.g., cerebrovascular accident or transient ischemic attacks) within the past 6 months * No signs or symptoms of vascular insufficiency (i.e., any history of blood clots or other ischemic peripheral vascular disease) * No evidence or history of bleeding diathesis or coagulopathy * No pulmonary hemorrhage or bleeding event ≥ CTCAE grade 2 within the past 4 weeks * No other hemorrhage or bleeding event ≥ CTCAE grade 3 within the past 4 weeks * No serious nonhealing wound, ulcer, or bone fracture * No significant traumatic injury within the past 4 weeks * No condition that impairs the patient's ability to swallow whole pills * No malabsorption problem * No known history of allergic reactions and/or hypersensitivity to melphalan, sorafenib tosylate, or any other agent used in the study * No psychiatric condition or diminished capacity that would compromise giving informed consent, or interfere with study compliance * No history of other malignancies, except for any of the following: * Adequately treated basal cell or squamous cell carcinoma of the skin * Curatively treated in situ carcinoma of the uterine cervix, prostate cancer, or superficial bladder cancer * Other curatively treated solid tumor with no evidence of disease for ≥ 5 years PRIOR CONCURRENT THERAPY: * Recovered from prior therapy * No prior sorafenib tosylate * Prior melphalan via isolated limb infusion allowed * No antineoplastic therapy, radiotherapy, or any other investigational drug within the past 4 weeks * No major surgery or open biopsy within the past 4 weeks * No concurrent Hypericum perforatum (St. John wort) or rifampin * Concurrent anti-coagulation treatment with warfarin or heparin allowed