Sunitinib and Chemoembolization in Treating Patients With Liver Cancer That Cannot Be Removed by Surgery

DISEASE CHARACTERISTICS: * Histologically, cytologically, or serologically\* confirmed hepatocellular carcinoma meeting the following criteria: * 1-4 lesions * Involvement of 1 or both liver lobes NOTE: \*Alpha-fetoprotein (AFP) \> 500 mcg/L in high-risk patients * Measurable disease by CT scan or MRI * Disease does not exceed 50% of the liver parenchyma * At least 1 lesion ≥ 3 cm in longest diameter * Tumor burden involves \< 50% of the liver * Refused surgery OR unresectable disease due to any of the following: * Multifocality * Advanced cirrhosis * Comorbid illness * Candidate for chemoembolization * No fibrolamellar histology * No ascites * No known brain metastases PATIENT CHARACTERISTICS: * ECOG performance status 0-2 * Life expectancy ≥ 12 weeks * WBC ≥ 3,000/mm³ * ANC ≥ 1,500/mm³ * Hemoglobin ≥ 8.5 g/dL (transfusion allowed) * Platelet count ≥ 100,000/mm³ * Bilirubin ≤ 2 mg/dL * AST ≤ 5 times upper limit of normal (ULN) * INR \< 1.5 * Creatinine ≤ 2.0 mg/dL OR creatinine clearance ≥ 30 mL/min * No bleeding diathesis or coagulopathy * No active congestive heart failure * No uncontrolled angina * No myocardial infarction within the past 12 months * No cardiac arrhythmia * Ejection fraction ≥ 45% (in patients with known coronary artery disease and in patients \> 50 years of age) * Child-Pugh class A or B cirrhosis * No impedance of hepatopedal blood flow (portal vein thrombosis) * No thrombosis of the main portal vein * No encephalopathy * No biliary obstruction * No variceal bleed within the past 6 months * No history of allergic reactions attributed to compounds of similar chemical or biologic composition to sunitinib malate * No absolute contraindication to doxorubicin, iodinated contrast material, microfibrillar collage hemostat, or dexamethasone * No other concurrent uncontrolled illness including, but not limited to, any of the following: * Ongoing or active infection * Psychiatric illness or social situation that would limit compliance with study requirements * No other active malignancies within the past year except nonmelanoma skin cancer or carcinoma in situ * No significant traumatic injury within the past 4 weeks * No QTc prolongation (i.e., QTc interval ≥ 500 msec) or other significant ECG abnormalities * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for 6 months after the completion of study treatment PRIOR CONCURRENT THERAPY: * Recovered from prior therapy * Prior liver-directed therapy, such as chemoembolization, radiofrequency ablation, cryoablation, or ethanol injection allowed if the following criteria are met: * Treated lesion remains inactive by CT scan or MRI and new lesion being embolized is distinct from the previously treated lesion * Radiographic progression of previously treated lesion requiring re-embolization * Prior liver resection allowed * Prior immunotherapy allowed * No prior antiangiogenesis therapy * No prior liver transplantation * Patients awaiting a cadaveric or orthotopic liver transplantation are eligible provided they have end-stage liver disease with a priority score of \< 20 points * More than 4 weeks since prior radiotherapy or chemotherapy (6 weeks for nitrosoureas or mitomycin C) * More than 4 weeks since prior major surgery or open biopsy * At least 1 week since prior fine needle biopsy * No concurrent immunotherapy * No concurrent radiotherapy * No concurrent combination antiretroviral therapy for HIV-positive patients * No concurrent therapeutic doses of coumarin-derivative anticoagulants (e.g., warfarin) * Doses of ≤ 1 mg/day are allowed for prophylaxis of thrombosis as long as INR ≤ 1.5 * Both full dose and prophylactic dose low molecular weight heparin allowed as long as PT INR ≤ 1.5 * No anticipated major surgery during and for 3 months after completion of study treatment * No other concurrent investigational agents * No other concurrent anticancer therapy