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 placement of central venous catheter (femoral, subclavian)

Exclusion Criteria:

* Patients who are human immunodeficiency virus positive (HIV+)
* GROUP 1: (PATIENTS AGED \> 65 AND \< 75 YEARS)
* Patients unwilling to use contraceptive techniques during and for 12 months following treatment
* Presence of circulating leukemic blasts (in the peripheral blood) detected by standard pathology for patients with CML
* Patients in an interferon induced complete or partial cytogenetic remission
* Organ dysfunction:

  * Patients with renal failure are eligible, however patients with renal compromise (Serum creatinine greater than 2.0) will likely have further compromise in renal function and may require hemodialysis (which may be permanent) due to the need to maintain adequate serum cyclosporine levels
  * Cardiac ejection fraction \< 40%; ejection fraction is required if the patient has a history of anthracyclines or history of cardiac disease
  * Diffusing capacity of the lung for carbon monoxide (DLCO) \< 50% of predicted
  * Liver function tests including total bilirubin, serum glutamic pyruvate transaminase (SGPT) and serum glutamic oxaloacetic transaminase (SGOT) \> 2x the upper limit of normal unless proven to be due to the malignancy
  * Karnofsky score \< 70
* Patients with poorly controlled hypertension
* GROUP 2 (PATIENTS AGED =\< 65)
* Patients who are HIV+
* Presence of circulating leukemic blasts (in the peripheral blood) detected by standard pathology for patients with CML
* Females who are pregnant
* Patients unwilling to use contraceptive techniques during and for 12 months following treatment
* Patients in an interferon induced complete or partial cytogenetic remission
* Organ dysfunction:

  * Patients with renal failure are eligible, however patients with renal compromise (Serum creatinine greater than 2.0) will likely have further compromise in renal function and may require hemodialysis (which may be permanent) due to the need to maintain adequate serum cyclosporine levels
  * Cardiac ejection fraction \< 40% or a history of congestive heart failure; ejection fraction is required if the patient has a history of anthracyclines or history of cardiac disease
  * Severe defects in pulmonary function testing as defined by the pulmonary consultant (defects are currently categorized as mild, moderate and severe) or receiving supplementary continuous oxygen; DLCO \< 50% of predicted
  * Liver function tests: total bilirubin \> 2x the upper limit of normal, SGPT and SGOT 4x the upper limit of normal
  * Karnofsky score \< 50
* Patients with poorly controlled hypertension
* DONOR: Age less than 12 years
* DONOR: Pregnancy
* DONOR: Infection with HIV
* DONOR: Inability to achieve adequate venous access
* DONOR: Known allergy to G-CSF
* DONOR: Current serious systemic illness