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

      * Patients treated with azacitidine or decitabine who achieve a leukemia-free state are eligible (may have required up to 4 courses of therapy to reach this status)
    * Age 60 to 74 years
* Donors must meet the following criteria:

  * One of the following:

    * HLA-identical sibling (6/6) by serologic typing for class (A, B) and low-resolution molecular typing for class II (DRB1)
    * Matched unrelated donor (8/8) by high-resolution molecular typing at HLA-A, -B, -C, and DRB1
  * No syngeneic donors
* Eastern Cooperative Oncology Group (ECOG) performance status 0-2
* Calculated creatinine clearance ≥ 40 mL/min
* Bilirubin \< 2 mg/dL OR bilirubin 2-3 mg/dL provided direct bilirubin is normal
* Aspartate aminotransferase (AST) \< 3 times upper limit of normal
* Diffusing capacity of the lung for carbon monoxide (DLCO) \> 40% with no symptomatic pulmonary disease
* Left ventricle ejection fraction (LVEF) \>= 30% by echocardiogram (ECHO) or multigated acquisition (MUGA)
* Not pregnant or nursing
* Negative pregnancy test
* Fertile patients must use effective contraception
* No uncontrolled diabetes mellitus or active serious infections
* No known hypersensitivity to E. coli-derived products, azacitidine, or mannitol
* No human immunodeficiency virus (HIV) infection or active hepatitis B or C
* Prior azacitidine or decitabine allowed

  * No patients who progressed from MDS to AML during treatment with azacitidine or decitabine
* At least 4 weeks since prior deoxyribonucleic acid (DNA)-hypomethylating chemotherapy, radiotherapy, and/or surgery
* No more than 2 courses of consolidation therapy before transplantation (for patients with AML)

  * Any consolidation regimen that does not require transplantation can be used
  * No more than 6 months from documentation of morphologic CR to transplantation