Treo/Flu/TBI With Donor Stem Cell Transplant for Patients With Myelodysplastic Syndrome or Acute Myeloid Leukemia

Inclusion Criteria: * MDS, myelodysplastic syndrome/myeloproliferative neoplasia overlap disorders (including chronic myelomonocytic leukemia \[CMML\], and MDS/myeloproliferative neoplasm \[MPN\] unclassifiable syndromes) * AML, other than acute promyelocytic leukemia (APL), in first or second remission or with minimal residual disease * With Karnofsky index or Lansky Play-Performance scale \> 70% on pre-transplant evaluation * Able to give informed consent (if \> 18 years), or with a legal guardian capable of giving informed consent (if \< 18 years) * Patients with previous autologous or allogeneic HCT are allowed to enroll * DONOR: Human leukocyte antigen (HLA)-identical related donors or * DONOR: Unrelated donors matched for HLA-A, B, C, DRB1, and DQB1 as defined by high resolution deoxyribonucleic acid (DNA) typing; mismatch for one HLA allele is allowed * DONOR: Donors able to undergo peripheral blood stem cell collection or bone marrow harvest * DONOR: Donors in good general health, with a Karnofsky or Lansky play performance score \> 90% * DONOR: Donors able to give informed consent (if \> 18 years), or with a legal guardian capable of giving informed consent (if \< 18 years) Exclusion Criteria: * Receiving umbilical cord blood * With impaired cardiac function as evidenced by ejection fraction \< 35% (or, if unable to obtain ejection fraction, shortening fraction of \< 26%) or cardiac insufficiency requiring treatment or symptomatic coronary artery disease; patients with a shortening fraction \< 26% may be enrolled if approved by a cardiologist * With impaired pulmonary function as evidenced by partial pressure of oxygen (pO2) \< 70 mm Hg and carbon monoxide diffusing capability test (DLCO) \< 70% of predicted or pO2 \< 80 mm Hg and DLCO \< 60% of predicted; (or, for pediatric patients unable to perform pulmonary function tests, then oxygen (O2) saturation \< 92% on room air), or receiving supplementary continuous oxygen * With impaired renal function as evidenced by creatinine-clearance \< 50% for age, weight, height or serum creatinine \> 2 x upper limit of normal or dialysis-dependent * With hepatic dysfunction as evidenced by total bilirubin \> 2.0 x upper limit of normal or evidence of synthetic dysfunction or severe cirrhosis * With hepatic dysfunction as evidenced by aspartate aminotransferase (AST) \> 2.0 x upper limit of normal or evidence of synthetic dysfunction or severe cirrhosis * With active infectious disease requiring deferral of conditioning, as recommended by an infectious disease specialist * With human immunodeficiency virus (HIV)-positivity or active infectious hepatitis * With central nervous system (CNS) leukemic involvement not clearing with intrathecal chemotherapy, cranial irradiation or both prior to initiating conditioning (day -6) * Patients with active non-hematological malignancies (except non-melanoma skin cancers) or those with non-hematological malignancies who have been rendered with no evidence of disease, but have a greater than 20% chance of having disease recurrence within 5 years; this exclusion does not apply to patients with non-hematologic malignancies that do not require therapy * With life expectancy severely limited by diseases other than malignancy * Women who are pregnant or lactating * With known hypersensitivity to treosulfan or fludarabine (fludarabine phosphate) * Receiving another experimental drug within 4 weeks before initiation of conditioning (day -6) * Unable to give informed consent (if \> 18 years) or with a legal guardian (if \< 18 years) unable to give informed consent * DONOR: Individuals deemed unable to undergo marrow harvesting or PBSC mobilization and leukapheresis * DONOR: Individuals who are HIV-positive * DONOR: Individuals with active infectious hepatitis * DONOR: Females with a positive pregnancy test * DONOR: Persons unable to give informed consent (if \> 18 years) or with a legal guardian (if \< 18 years) unable to give informed consent