Belinostat and Azacitidine in Treating Patients With Advanced Hematologic Cancers or Other Diseases

Inclusion Criteria: * Histologically confirmed diagnosis of 1 of the following: * Relapsed or refractory acute myeloid leukemia (AML) * Relapsed or refractory acute promyelocytic leukemia (must have failed both tretinoin and arsenic trioxide) * Relapsed or refractory acute lymphoblastic leukemia * Secondary AML, including AML arising from antecedent hematologic diseases, such as myelodysplastic syndromes (MDS) or myeloproliferative disorders, OR therapy-related AML * Chronic myelogenous leukemia in accelerated or blast phase * Advanced phases of Philadelphia chromosome-negative (Ph-) chronic myeloproliferative disorders, as defined by ≥ 1 of the following: * Presence of anemia (hemoglobin \< 10 g/dL and/or red blood cell transfusion dependent) * Presence of palpable splenomegaly * MDS, including chronic myelomonocytic leukemia * Must have intermediate or high-risk International Prognostic Scoring System (IPSS) scores (≥ 0.5) * Low-risk IPSS scores allowed provided ≥ 1 of the following criteria are met: * Hemoglobin \< 10 g/dL and/or red blood cell transfusion dependent * Platelet count \< 50,000/mm³ * Absolute neutrophil count \< 1,000/mm³ * Refractory disease OR no standard therapy exists * Evidence of AML associated with dysplasia on bone marrow histology for elderly patients (i.e., \> 60 years old) who are previously untreated and not candidates for or unwilling to undergoing induction therapy * No known active CNS involvement with disease * CALGB performance status (PS) 0-2 OR Karnofsky PS 60-100% * Bilirubin ≤ 2.0 mg/dL (unless due to Gilbert's syndrome) * ALT ≤ 3 times upper limit of normal (unless due to disease) * Creatinine ≤ 2 mg/dL * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No history of allergic reactions attributed to compounds of similar chemical or biologic composition to PXD101 or Azacitidine * No history of allergic reactions to mannitol * No history of dose-limiting toxicity during prior treatment with Azacitidine * No concurrent uncontrolled illness including, but not limited to, the following: * Ongoing or active infection * Symptomatic congestive heart failure * Unstable angina pectoris * Cardiac arrhythmia * Psychiatric illness or social situation that would preclude compliance with study requirements * No marked baseline prolongation of QT/QTc interval (e.g., repeated demonstration of a QTc interval \> 500 msec) * No long QT syndrome * No uncontrolled cardiovascular disease, including the following: * Severe uncontrolled hypertension * Uncontrolled congestive heart failure related to primary cardiac disease * Uncontrolled cardiac arrhythmia * Uncontrolled ischemic or severe valvular heart disease * Myocardial infarction within the past 6 months * See Disease Characteristics * Recovered from prior therapy * At least 2 weeks since prior chemotherapy (6 weeks for mitomycin C or nitrosoureas) * At least 2 weeks since prior radiotherapy * At least 4 weeks since prior investigational agents * At least 24 hours since prior hydroxyurea * At least 2 weeks since prior valproic acid * No concurrent combination antiretroviral therapy for HIV-positive patients * No other concurrent investigational agents * No concurrent medication that may cause torsade de pointes * No other concurrent anticancer therapy, including chemotherapy, radiotherapy, or biological agents