Treosulfan, Fludarabine Phosphate, and Total-Body Irradiation in Treating Patients With Hematological Cancer Who Are Undergoing Umbilical Cord Blood Transplant

Inclusion Criteria: * Acute myeloid leukemia/acute lymphoblastic leukemia, including biphenotypic acute leukemia or mixed-lineage leukemia: Must have \< 5% morphologic marrow blasts in an evaluable marrow sample (\> 25% of normal cellularity for age collected less than one month prior to start of conditioning; patients in which adequate marrow/biopsy specimens cannot be obtained to determine remission status by morphologic assessment, but have fulfilled criteria of remission by flow cytometry, recovery of peripheral blood counts with no circulating blasts, and/or normal cytogenetics (if applicable) may still be eligible; reasonable attempts must be made to obtain an adequate specimen for morphologic assessment, including possible repeat procedures; these patients must be discussed with the principal investigator prior to enrollment; patients persistently aplastic for greater than one month since completing last chemotherapy are also eligible with principal investigator (PI) approval * Myelodysplastic syndrome (MDS): Any 2001 World Health Organization (WHO) classification subtype; refractory anemia with excess blasts (RAEB)-2 patients may proceed directly to transplant, but may also be considered for induction chemotherapy before transplant; patients with \>= 20% morphologic marrow blasts require induction therapy to reduce morphologic marrow blasts below 5% before transplant * Chronic myelogenous leukemia: All types, except refractory blast crisis; chronic phase patients mus…