Transarterial Chemoembolization With Doxorubicin With or Without Everolimus in Treating Patients With Liver Cancer

DISEASE CHARACTERISTICS: * Histologically, cytologically, or radiologically confirmed hepatocellular carcinoma * Intermediate stage B (according to Barcelona Clinic Liver Cancer classification) * Child-Pugh score \< 8 * No tumor involvement \> 50% of whole liver * No advanced stage disease (i.e., either portal invasion \[segmental portal obstruction\] or extrahepatic spread) * No presence or history of metastatic disease * Candidate for transarterial chemoembolization after multidisciplinary discussion (tumor board) * Not on an active waiting list for liver transplantation PATIENT CHARACTERISTICS: * WHO performance status 0-1 * Hemoglobin ≥ 90 g/L * Absolute neutrophil count ≥ 1.5 x 10\^9/L * Platelet count ≥ 100 x 10\^9/L * Bilirubin ≤ 1.5 x upper limit of normal (ULN) * ALT ≤ 4 x ULN * INR ≤ 2 * Creatinine ≤ 1.5 x ULN * Not pregnant or nursing * Fertile patients must use effective contraception during and for 12 months after completion of study therapy * Negative pregnancy test * None of the following contraindications: * Complete portal vein thrombosis * Large arterio-portal or arterio-venous fistula within the liver * Allergy to contrast media * Contraindication to hepatic artery catheterization, such as severe peripheral vascular disease precluding catheterization * No active heart disease, including any of the following: * NYHA class II-IV congestive heart failure * Active coronary artery disease (myocardial infarction \> 6 months prior to trial entry allowed) * Cardiac arrhythmias requiring anti-arrhythmic therapy (beta-blockers or digoxin permitted) * Uncontrolled hypertension * No hypertension, defined as systolic blood pressure (BP) \> 150 mm Hg or diastolic BP \> 90 mm Hg despite optimal medical management * No thrombotic or embolic events within the past 6 months including any of the following: * Cerebrovascular accident (including transient ischemic attacks) * Pulmonary embolism * Deep vein thrombosis * No serious non-healing wounds, including wounds healing by secondary intention, acute or non-healing ulcers, or bone fractures within 3 months of fracture * No evidence of bleeding diathesis * No history of hemoptysis * No clinically serious infection \> grade 2 (NCI CTCAE Version 3.0) except for HBV and HCV infection * No known HIV infection * No CTCAE acute adverse events grade \> 2 after prior TACE therapy * No other prior or concurrent malignancy that is distinct in primary site or histology from HCC, except carcinoma in situ of the cervix, treated nonmelanoma skin cancer, superficial bladder tumor (Ta, Tis, T1), or any cancer curatively treated \> 3 years prior to entry * No psychiatric disorder precluding understanding of information on trial related topics, giving informed consent, filling out QL forms, or interfering with compliance for oral drug intake * No serious underlying medical condition, at the judgment of the investigator, which could impair the ability of the patient to participate in the trial (e.g., active autoimmune disease, uncontrolled diabetes) * No known hypersensitivity to trial drugs or hypersensitivity to any other component of the trial drugs * No contraindication to have MRI (e.g., pacemaker) * No organ allograft * No known impairment of swallowing that would preclude administration of everolimus * Completed baseline quality of life, BL-HEA, and EQ5D questionnaires (Phase II only) * Able to comply and have geographic proximity to allow proper staging and follow-up PRIOR CONCURRENT THERAPY: * At least 4 weeks since prior transarterial embolization/chemoembolization \[limited to 5 treatments\], radiofrequency ablation, cryoablation, radiation therapy or percutaneous ethanol injection * At least 4 weeks since prior sorafenib * At least 30 days since treatment with other experimental drugs or other anticancer therapy, or treatment in another clinical trial * At least 30 days since use of biologic response modifiers (e.g., G-CSF and other hematopoietic growth factors) * More than 4 weeks since prior and no concurrent major surgery * More than 3 weeks since prior and no concurrent radiotherapy * Concurrent erythropoietin allowed provided no dose adjustment is undertaken within 1 month prior to the trial or during the trial * No concurrent anticancer drugs (e.g., bevacizumab, and any drugs that target VEGF or VEGF receptors) * No concurrent investigational drugs * No concurrent known strong CYP3A4 inhibitors (e.g., ketoconazole, fluconazole, itraconazole, voriconazole, erythromycin, clarithromycin, diltiazem, verapamil, and protease inhibitors) * No concurrent known strong CYP3A4 inducers (e.g., carbamazepine, continuous treatment with dexamethasone \[\> 2 mg/day for \> 7 days\], phenobarbital, phenytoin, rifampicin, and St. John's wort) * No concurrent grapefruit, grapefruit juice, and products containing bitter oranges * No concurrent systemic corticosteroids (e.g., \> 1 mg/kg prednisolone) for more than 2 weeks * No concurrent angiotensin converting enzyme inhibitors (ACE-I)