Fludarabine Phosphate and Total-Body Irradiation Followed by Donor Peripheral Blood Stem Cell Transplant in Treating Patients With Acute Lymphoblastic Leukemia or Chronic Myelogenous Leukemia That Has Responded to Treatment With Imatinib Mesylate, Dasatinib, or Nilotinib

Inclusion Criteria: * Patients =\< 12 years of age must be approved by Fred Hutchinson Cancer Research Center (FHCRC) principal investigator (PI) in advance * Patients with a history of Ph+ ALL or CML-BC who, after receiving imatinib mesylate, (or either dasatinib or nilotinib) have \< 15% blasts on morphologic marrow evaluation; patients with no detectable Ph+ ALL by morphologic or molecular assays (complete remission) will be accepted * An appropriately human leukocyte antigen (HLA) matched related or unrelated donor must be prospectively identified who will be available to donate filgrastim (G-CSF) mobilized stem cells * RELATED DONOR: * Related donor who is HLA genotypically identical at least at one haplotype and may be genotypically or phenotypically identical at the allele level at HLA-A, -B, -C, -DRB1, and -DQB1; * Donor must consent to G-CSR administration and leukapheresis; * Donor must have adequate veins for leukapheresis or agree to placement of central venous catheter (femoral, subclavian) * HLA-MATCHED UNRELATED DONOR: * FHCRC matching allowed will be grades 1.0 to 2.1; unrelated donors who are prospectively matched for HLA-A, B, C, DRB1 and DQB1 by high resolution typing; only a single allele disparity will be allowed for HLA-A, B, or C as defined by high resolution typing * A positive anti-donor cytotoxic crossmatch is an absolute donor exclusion; donors are excluded when preexisting immunoreactivity is identified that would jeopardize donor hema…