Panobinostat and Sorafenib in Treating Patients With Liver Cancer That is Metastatic and/or Cannot Be Removed by Surgery

DISEASE CHARACTERISTICS: * Histologically or cytologically confirmed hepatocellular carcinoma * Metastatic and/or unresectable disease * Child-Pugh score A or B PATIENT CHARACTERISTICS: * ECOG performance status 0-2 * Neutrophil count \> 1500/mm³ * Platelet count \> 100,000/mm³ * Hemoglobin ≥ 9 g/dL * AST and ALT ≤ 2.5 times upper limit of normal (ULN) (≤ 5.0 times ULN if elevation due to disease involvement) * Serum bilirubin ≤ 1.5 times ULN * Serum creatinine ≤ 1.5 times ULN or creatinine clearance ≥ 50 mL/min * Total serum calcium (corrected for serum albumin) or ionized calcium ≥ lower limit of normal (LLN) * Serum potassium ≥ LLN * Serum sodium ≥ LLN * Serum albumin ≥ LLN or 3 g/dL * LVEF ≥ LLN as demonstrated by baseline MUGA or ECHO * TSH and free T4 within normal limits (thyroid hormone replacement therapy allowed) * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective double-method contraception (one being a barrier method) during and for 3 months after completion of study treatment * INR \< 1.5 or PT/PTT within normal limits * No impaired cardiac function including any 1 of the following: * QTc \> 450 msec on screening ECG * Congenital long QT syndrome * History of sustained ventricular tachycardia * History of ventricular fibrillation or torsades de pointes * Bradycardia, defined as heart rate \< 50 beats per minute * Patients with a pacemaker and heart rate ≥ 50 beats per minute are eligible * Myocardial infarction or unstable angina within the past 6 months * Congestive heart failure (NYHA class III-IV) * Right bundle branch block and left anterior hemiblock (bifascicular block) * No uncontrolled hypertension * No thrombolic or embolic events (e.g., cerebrovascular accident and transient ischemic attacks) within the past 6 months * No pulmonary hemorrhage/bleeding event \> CTCAE Grade 2 within the past 4 weeks * No other hemorrhage/bleeding event \> CTCAE Grade 3 within the past 4 weeks * No unresolved diarrhea \> CTCAE grade 1 * No other concurrent severe and/or uncontrolled medical conditions * No other primary malignancy within the past 5 years except curatively treated carcinoma in situ of the cervix or basal cell or squamous cell carcinoma of the skin * No serious non-healing wound, ulcer, or bone fracture * No evidence or history of bleeding diathesis or coagulopathy * No significant traumatic injury within the past 4 weeks * No known or suspected allergy to sorafenib tosylate or any other study drug * No condition that would impair a patient's ability to swallow whole pills * No malabsorption problem * No known human immunodeficiency virus (HIV) or hepatitis C positivity (baseline testing for HIV and hepatitis C is not required) * No significant history of non-compliance to medical regimens PRIOR CONCURRENT THERAPY: * No prior HDAC inhibitors, DAC inhibitors, HSP90 inhibitors, sorafenib tosylate, or valproic acid for the treatment of cancer * More than 4 weeks since prior chemotherapy, investigational drugs, or major surgery and recovered * More than 4 weeks since open biopsy * More than 5 days since prior and no concurrent valproic acid for any medical condition * No concurrent St. John's wort or rifampin * No concurrent drugs with a risk of causing torsades de pointes * No concurrent CYP3A4 inhibitors * No concurrent radiotherapy * No concurrent grapefruit, grapefruit juice, or Seville (sour) oranges * No other concurrent investigational therapy * No other concurrent anticancer agents * Concurrent anticoagulation treatment with warfarin or heparin allowed