PXD101 as Second-Line Therapy in Treating Patients With Malignant Mesothelioma of the Chest That Cannot Be Removed By Surgery

Inclusion Criteria: * Histologically or cytologically confirmed malignant pleural mesothelioma (MPM) of any of the following subtypes: * Epithelial * Sarcomatoid * Mixed * Have received only 1 prior systemic chemotherapy regimen for advanced mesothelioma * Prior intrapleural cytotoxic agents (including bleomycin) not considered systemic chemotherapy * Patients who are not candidates for combination chemotherapy are eligible even if they have not received prior chemotherapy * Unresectable disease * Measurable disease, defined as \>= 1 unidimensionally measurable lesion \>= 20 mm by conventional techniques OR \>= 10 mm by spiral CT scan * The sole site of measurable disease must not be located within the radiotherapy port * No known brain metastases * ECOG performance status (PS) 0-2 OR Karnofsky PS 60-100% * Life expectancy \> 3 months * WBC \>= 3,000/mm\^3 * Absolute neutrophil count \>= 1,500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Bilirubin normal * AST/ALT =\< 2.5 times upper limit of normal * Creatinine normal OR creatinine clearance \>= 50 mL/min * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective double-barrier contraception for 1 week before, during, and for \>= 2 weeks after completion of study treatment * No history of allergic reactions attributed to compounds of similar chemical or biologic composition to PXD101 * No symptomatic congestive heart failure * No congestive heart failure related to primary cardiac disease * No unstable angina pectoris * No cardiac arrhythmia * No condition requiring anti-arrhythmic therapy * No uncontrolled hypertension * No myocardial infarction within the past 6 months * No ischemic or severe valvular heart disease * No ongoing or active infection * No marked baseline prolongation of QT/QTc interval * No repeated QTc interval \> 500 msec * No long QT syndrome * No other significant cardiovascular disease * No other uncontrolled intercurrent illness * No psychiatric illness or social situation that would preclude study compliance * Recovered from prior therapy * No prior valproic acid or other known histone deacetylase (HDAC) inhibitor * More than 3 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin C) * More than 3 weeks since prior radiation therapy * No concurrent medication that may cause torsade de pointes * No concurrent combination antiretroviral therapy for HIV-positive patients * No other concurrent investigational agents * No other concurrent anticancer agents or therapies