FR901228 in Treating Patients With Relapsed or Refractory Multiple Myeloma

Inclusion Criteria: * Patients must have histologically or cytologically confirmed stage IIa or IIIa multiple myeloma * Patient has progressive disease and has had 1, 2, 3, or 4 prior lines of therapy * Bilirubin \< 2.0 mg/dL * SGOT/SGPT =\< 2.5 X institutional upper limit of normal * Serum creatinine =\< 1.5 mg/dl OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Karnofsky Performance Status equal or greater than 70%; KPS 60% will be allowed if reduced KPS is due to advanced skeletal disease * Measurable disease as defined by serum M protein \>= 1.0 gm/dl measured by serum protein electrophoresis or free light chain measurement, or quantitative immunoglobulins and/or urinary M protein excretion \>= 200 mg/24 hrs * Ejection fraction \>= 50% and normal baseline EKG tracing * No known central nervous system abnormality including neoplastic, vascular, inflammatory, degenerative or epilepsy * Life expectancy of greater than 12 weeks * Leukocytes \>= 3,000/uL * Absolute neutrophil count \>= 1,500/uL * Platelets \>= 100,000/uL * Patients in whom cytopenias are considered to be due to myeloma marrow infiltration will be allowed as long as they meet the following criteria: * Bone marrow biopsy displaying \>= normal cellularity for age and \>= 50% involvement by myeloma * ANC \> 1,000 and platelets \> 50,000 * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign written informed consent Exclusion Criteria: * Administration of chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to enrollment or unresolved adverse events due to agents administered more than 4 weeks earlier * Prior treatment with a histone deacetylase inhibitor * Patients may not be receiving any other investigational agent * History of second cancer (except for adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, or other cancer for which the patient has been disease free \>= 5 years) * Non secretory disease or plasma cell leukemia (\> 2000 circulating plasma cells/uL) * History of allergic reactions attributed to compounds of similar chemical or biologic composition to depsipeptide * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Patients with left ventricular hypertrophy or history of arrhythmias including atrial fibrillation, myocardial infarction or congestive heart failure; patients may not be taking hydrochlorothiazides * Patients that are pregnant or lactating will be excluded from this trial * Known HIV positivity; patients infected with the HIV virus will be excluded from this trial