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 invol…