Fludarabine and 400 CGY Total Body Irradiation for Recipients of HLA-Matched or Mis-Matched Family or Unrelated Donor Hematopoietic Stem Cell Transplants Who Have Rejected Their First Allogeneic Stem Cell Transplant

Inclusion Criteria: Any patient who has rejected a previous allogeneic transplant (related or unrelated) rejection based on chimerism data from peripheral blood specimens showing loss of donor T Cells. 1. Available HLA-identical, a one-antigen mis-matched sibling donor, a phenotypically HLA-matched family member, a phenotypically matched unrelated donor, or a 9/10 matched unrelated donor with a negative cross-match. 2. Age ≤ 75 years. 3. Patients who fail to engraft or have signs of early relapse after an autologous transplant may be considered for this protocol as salvage treatment if they are presented to the RMBMTP Clinical Care meeting and the majority of the group agrees that this a reasonable treatment option. Exclusion Criteria: 1. Patients whose low donor chimerism is felt to be due to rapidly progressive hematological malignancies, unless they can be treated into a minimal disease state with additional treatment. 2. Patients with active uncontrolled CNS involvement with malignancy. 3. Fertile men or women unwilling to use contraceptive techniques during and for 12 months following treatment. 4. Females who are pregnant. 5. Patients who are HIV positive 6. Organ dysfunction felt to be due to the conditioning for the first transplant including the following: * Left ventricle ejection fraction \< 35%. * DLCO \<35% of predicted, or receiving continuous supplementary oxygen. * Karnofsky score \<50 for patients \< 60 years, or \<70 for patients aged 60 - 69 years (see appendix B). * Creatinine clearance \< 40 ml/min. * Patients with these end-organ toxicities may be presented to the RMBMTP Patient Care Conference. If the majority opinion is that this treatment is the safest option for a patient who has rejected their first transplant, they will be allowed to undergo the treatment, after informed consent has been signed. * Patients with a positive PRA or anti-donor T or B cell (+) will be considered for this treatment protocol only if no other option is available. They should not be eligible for another research study. The transplantation group must have a majority opinion that this is the best available option for the patient in question. In patients with either condition, the only acceptable stem cell source will be peripheral blood.