Sorafenib Tosylate With or Without Everolimus in Treating Patients With Localized, Unresectable, or Metastatic Liver Cancer

DISEASE CHARACTERISTICS: * Histologically, cytologically, or radiologically confirmed hepatocellular carcinoma (HCC) * Localized, unresectable, or metastatic disease * Child-Pugh class A or mildly decompensated Child-Pugh class B liver dysfunction (Child-Pugh score ≤ 7) * Stage B or C disease according to the Barcelona Clinic Liver Cancer (BCLC) staging classification * Measurable disease * At least 1 unidimensionally measurable site of disease (≥ 10 mm in case of a non-nodal lesion or with a short axis ≥ 15 mm in case of a lymph node) by spiral/multi-slice CT/MRI scan according to revised RECIST criteria * No locally advanced disease AND a candidate for radical surgery * No known fibrolamellar HCC or mixed cholangiocarcinoma/HCC * No clinical symptoms or history of CNS metastases or leptomeningeal disease (no imaging required) PATIENT CHARACTERISTICS: * WHO performance status 0-1 * Hemoglobin ≥ 90 g/L * Neutrophil count ≥ 1.5 x 10\^9/L * Platelet count ≥ 75 x 10\^9/L * Creatinine clearance ≥ 40 mL/min * ALT ≤ 5 times upper limit of normal * INR ≤ 2 * Urine dipstick for proteinuria ≤ 1+ OR protein spot urine \< 0.6 g/L * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for 12 months after completion of study therapy * No prior malignancy within the past 5 years except adequately treated carcinoma in situ of the cervix or localized nonmelanoma skin cancer * No history of hemorrhagic or thrombotic cerebrovascular event within the past 12 months * No documented variceal hemorrhage within the past 3 months * No requirement for anticoagulant therapy except for low-dose anticoagulants for maintenance of patency of central venous access or prevention of deep vein thrombosis * No history or presence of clinically significant acute or unstable cardiovascular, cerebrovascular, renal, gastrointestinal, pulmonary, endocrine, central nervous system, or immunological disorders (except for the presence of hepatitis B or C virus or cirrhosis) within the past 6 months * No encephalopathy * No known HIV infection * No active infection requiring IV antibiotics * No arterial hypertension ≥ 150/100 mm Hg despite therapy * No ongoing cardiac dysrhythmias of NCI CTCAE grade ≥ 2, atrial fibrillation of any grade, prolongation of QTc \> 500 msec on screening electrocardiogram (ECG), or history of familial long QT syndrome * No repeated paracentesis (more than 1 per month) * No psychiatric disorder precluding understanding of information of trial-related topics, giving informed consent, or interfering with compliance for oral drug intake * No concurrent grapefruit, grapefruit juice, or products containing bitter oranges * Able to take oral medications * Completed baseline quality of life questionnaire * Must be compliant and geographically proximal for follow-up PRIOR CONCURRENT THERAPY: * See Disease Characteristics * No prior systemic anticancer treatment for this disease * The following prior therapies are allowed provided previously treated lesions remain separate from those to be measured in the current trial and prior treatment is completed within the past 4 weeks * Surgery * Liver-directed therapy (e.g., transarterial embolization/chemoembolization \[limited to 5 treatments\], radiofrequency ablation, cryoablation, radiotherapy, or percutaneous ethanol injection) * No prior organ transplantation * No concurrent estrogen-containing supplementary therapy * No concurrent full-dose anticoagulation with coumarin derivatives * No concurrent elective major surgery * No concurrent radiotherapy (concurrent analgesic radiotherapy of non-target lesions allowed) * No concurrent or anticipated need for CYP3A4 inhibitors or inducers, unless the drugs are medically necessary and no substitutes are available, including any of the following: * Ketoconazole * Itraconazole * Voriconazole * Erythromycin * Clarithromycin * Diltiazem * Verapamil * Protease inhibitors * No concurrent strong CYP3A4 inducers\*, including any of the following: * Carbamazepine * Continuous dexamethasone (\> 2 mg/day for \> 7 days) * Phenobarbital * Phenytoin * Rifampicin * St. John's wort NOTE: \*Concurrent antacids allowed provided they are administered \> 1 hour before or \> 1 hour after trial drug administration. * No other concurrent experimental drugs or anticancer therapy or treatment in another clinical trial within the past 30 days * No other concurrent investigational drugs * No chronic systemic steroids or other immunosuppressive agents * No concurrent angiotension converting enzyme inhibitors (ACE-I)