Busulfan, Fludarabine Phosphate, and Anti-Thymocyte Globulin Followed By Donor Stem Cell Transplant and Azacitidine in Treating Patients With High-Risk Myelodysplastic Syndrome and Older Patients With Acute Myeloid Leukemia

Inclusion Criteria: * Meets one of the following sets of criteria: * Myelodysplastic syndromes (MDS): * Disease with high-risk features (found either at diagnosis or before initiation of cytotoxic therapy), defined as one of the following: * International prognostic scoring system (IPSS) risk \>= intermediate-2 * Refractory anemia with excess blasts by French-American-British (FAB) classification * High-risk cytogenetics (either complex or -7) * Less than 10% bone marrow blasts as determined by bone marrow biopsy within the past 4 weeks (reduction in marrow blast percentage may be achieved with chemotherapy or other therapy) * Less than 75 years old * Acute myeloid leukemia (AML): * No FAB M3 * No acute leukemia following blast transformation of prior chronic myelogenous leukemia or other myeloproliferative disease * Patients with preceding MDS or treatment-related AML are eligible * Prior central nervous system (CNS) involvement is allowed provided the disease is in remission at transplantation * Morphologic complete remission (leukemia-free state) is defined as meeting all of the following criteria: * Bone marrow blasts \< 5% (as determined by bone marrow within the past 4 weeks), but without requirement for normal peripheral blood counts * No extramedullary leukemia * No blasts in peripheral blood * Achieved complete remission (CR) after no more than 2 courses of induction chemotherapy …