Belinostat in Treating Patients With Liver Cancer That Cannot Be Removed By Surgery

Inclusion Criteria: * Histologically or cytologically confirmed hepatocellular carcinoma that is not amenable to curative resection * Measurable disease, defined as ≥ 1 lesion that can be accurately measured in ≥ 1 dimension (longest diameter to be recorded) as ≥ 20 mm with conventional techniques OR as ≥ 10 mm with MRI or spiral CT scan * No known brain metastases * No clinical ascites or encephalopathy * Life expectancy \> 12 weeks * ECOG performance status (PS) 0-2 or Karnofsky PS 60-100% * WBC ≥ 3,000/mm³ * Absolute neutrophil count ≥ 1,500/mm³ * Platelet count ≥ 100,000/mm³ * Bilirubin ≤ 1.7 mg/dL * Albumin ≥ 2.8 mg/dL * ALT ≤ 5.0 times upper limit of normal (ULN) * Alkaline phosphatase ≤ 6 times ULN * Prothrombin time ≤ 4 sec above ULN * Creatinine ≤ 1.6 mg/dL * Not pregnant or nursing * Negative pregnancy test * Fertile patients use effective contraception * No Child's-Pugh's grading Class C hepatic impairment * No history of allergic reaction attributed to compounds of similar chemical or biologic composition to PXD101 * No marked baseline prolongation of QT/QTc interval, including the following: * Repeated demonstration of a QTc interval \> 500 msec * Long QT Syndrome * No ongoing or active infection * No significant cardiovascular disease, including any of the following: * Unstable angina pectoris * Uncontrolled hypertension * Congestive heart failure related to primary cardiac disease * Condition requiring anti-arrhythmic therapy * Ischemic or severe valvular heart disease * Myocardial infarction within the past 6 months * No psychiatric illness or social situation that would preclude study compliance * No other uncontrolled illness * More than 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin C) and recovered * More than 4 weeks since prior radiotherapy and recovered * At least 2 weeks since prior valproic acid * No concurrent combination antiretroviral therapy for HIV-positive patients * No concurrent participation in another investigational study * No other concurrent investigational agents * No other concurrent anticancer therapy * No concurrent use of any of the following: * Disopyramide * Dofetilide * Ibutilide * Procainamide * Quinidine * Sotalol * Bepridil * Amiodarone * Arsenic trioxide * Cisapride * Calcium channel blockers (e.g., lidoflazine) * Clarithromycin * Erythromycin * Halofantrine * Pentamidine * Sparfloxacin * Domperidone * Droperidol * Chlorpromazine * Haloperidol * Mesoridazine * Thioridazine * Pimozide * Methadone