Fludarabine Phosphate, Low-Dose Total-Body Irradiation, and Peripheral Blood Stem Cell Transplant Followed by Donor Lymphocyte Infusion in Treating Older Patients With Chronic Myeloid Leukemia

Inclusion Criteria: * Patients with Philadelphia chromosome positive (Ph+) CML in first and second chronic and first accelerated phases * Patients =\< 65 years old who are at high risk of regimen related toxicity through pre-existing chronic disease affecting liver, lungs, and/or heart, or others who wish to be treated on this protocol, will be considered on a case-by-case basis; transplants should be approved for these inclusion criteria by both the participating institutions' patient review committees such as the Patient Care Conference (PCC) at the Fred Hutchinson Cancer Research Center (FHCRC) and by the principal investigators at the collaborating centers; patients =\< 65 years of age who have received previous high-dose transplantation do not require patient review committee approvals; all children \< 12 years must be discussed with the FHCRC principal investigator (PI) (Brenda Sandmaier, MD 206-667-4961) prior to registration * HLA genotypically identical related donor willing to undergo leukapheresis initially for collection of peripheral blood stem cell (PBSC) and subsequently for collection of peripheral blood mononuclear cell (PBMC) * Patients treated with alpha interferon must have discontinued drug at least 1 month prior to transplant * DONOR: HLA genotypically identical family member (excluding identical twins) * DONOR: Donor must consent to filgrastim (G-CSF) administration and leukapheresis * DONOR: Donor must have adequate veins for leukapheresis or agree to…