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…