Sorafenib Tosylate and Chemoembolization With Doxorubicin Hydrochloride and Mitomycin in Treating Patients With Liver Cancer That Cannot Be Removed By Surgery

DISEASE CHARACTERISTICS: * Diagnosis of hepatocellular carcinoma (HCC), as defined by 1 of the following: * Tissue histology * Recurrence of previously resected HCC does not require tissue confirmation if there is clear radiographic recurrence, in the judgment of the investigator * AFP \> 400 ng/mL with compatible mass on MRI * Locally advanced disease * Not eligible for surgical resection or immediate liver transplantation OR have refused such procedures * All disease must be amenable to embolization in one or two procedures * Measurable disease, according to modified HCC RECIST criteria * Must have radiographically documented measurable disease with at least one site of disease that is unidimensionally measurable as ≥ 10 mm on MRI * Lesions previously treated by radiofrequency ablation should not represent the only site of measurable disease * Childs-Pugh score ≤ 7 * No complete thrombosis of the main portal vein * If unilateral portal vein thrombosis is present, must demonstrate radiographic evidence of adequate flow to the lobe to be embolized * No evidence of extrahepatic/metastatic disease, such as lymph node metastases, lung or bone metastases, or peritoneal carcinomatosis * Evidence of cirrhosis is acceptable as long as the lab parameters are met * No known brain metastases PATIENT CHARACTERISTICS: * ECOG performance status 0-1 * Life expectancy ≥ 12 weeks * Hemoglobin ≥ 9.0 g/dL * ANC ≥ 1,500/mm³ * Platelet count ≥ 75,000/mm³ * Creatinine ≤ 1.5 times upper limit of normal (ULN) OR creatinine clearance ≥ 50 mL/min * Total bilirubin ≤ 3 mg/dL * ALT and AST ≤ 5 times ULN * INR \< 1.5 * Negative pregnancy test * Fertile patients must use effective contraception during and for ≥ 3 months after completion of study treatment * No other cancer within the past 3 years except for cervical carcinoma in situ, previously treated basal cell carcinoma, or superficial bladder tumors (Ta, Tis, or T1) * No NYHA class III or IV congestive heart failure * No unstable angina (anginal symptoms at rest) or new-onset angina within the past 3 months * No myocardial infarction within the past 6 months * No cardiac ventricular arrhythmias requiring anti-arrhythmic therapy * No uncontrolled hypertension (i.e., systolic BP \> 150 mm Hg or diastolic BP \> 90 mm Hg, despite optimal medical management) * No venous thrombotic or arterial embolic events (e.g., cerebrovascular accident, including transient ischemic attacks or venous thromboembolism) within the past 6 months * No pulmonary hemorrhage/bleeding event \> CTCAE grade 2 within the past 12 weeks * No other hemorrhage/bleeding event \> CTCAE grade 3 within the past 12 weeks * No variceal bleeding within past 12 weeks * No known grade 2 or 3 esophageal varices (endoscopic evaluation is not required for study entry) * No evidence or history of bleeding diathesis or coagulopathy * No significant traumatic injury within the past 12 weeks * No serious non-healing wound, ulcer, or bone fracture * No significant proteinuria (i.e., proteinuria \> 1+ on urine dipstick) * No HIV positivity (by patient report) * No active hepatitis B or C, unless patient has been on stable medications for ≥ 2 months * No active clinically serious infections (\> grade 2) * No active gastrointestinal malabsorption problem * No condition that would impair the patient's ability to swallow whole pills * No active drug or alcohol abuse * No known severe hypersensitivity or suspected allergy to sorafenib tosylate, any of its excipients, or other drugs used in this study * No psychological, familial, sociological, or geographical condition potentially hampering compliance with the study protocol and follow-up schedule PRIOR CONCURRENT THERAPY: * No prior systemic therapy, embolic therapy, or radiotherapy for HCC (e.g., chemotherapy, transarterial chemoembolization, transarterial embolization, or 90Y microspheres) * At least 4 weeks since prior liver resection or ablative therapy and recovered * No prior Raf/MEK/ERK-targeted therapy or VEGF-targeted therapy * More than 4 weeks since prior participation in any investigational drug study * More than 12 weeks since prior major surgery or open biopsy * Prior core liver biopsy allowed * No concurrent antiretroviral therapy for HIV * No concurrent chronic anticoagulation (other than 1 mg of warfarin daily for port patency) * No concurrent St. John wort or rifampin * No other concurrent anticancer therapy, radiotherapy, or investigational therapy