AlloHCT From Matched Unrelated Donors in Pts w/ Advanced Hematologic Malignancies & Disorders

RATIONALE: Giving chemotherapy with or without total-body irradiation before a donor umbilical cord blood transplant helps stop the growth of cancer or abnormal cells. It also helps stop the patient's immune system from rejecting the donor's stem cells. When the stem cells from a donor are infused into the patient they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells. Giving cyclosporine and mycophenolate mofetil before and after transplant may stop this from happening. PURPOSE: This clinical trial is studying how well four different chemotherapy regimens given with or without total-body irradiation before umbilical cord blood transplant work in treating patients with relapsed or refractory hematologic cancer.

OBJECTIVES: Primary * To determine the survival at day 100 of patients with relapsed, refractory, or poor-risk hematological malignancies treated with four different preparative regimens followed by allogeneic hematopoietic stem cell transplantation (HSCT) using two unrelated umbilical cord blood (UCB) units. Secondary * To determine the incidence and timing of neutrophil engraftment in patients treated with these regimens. * To determine the incidence and timing of platelet engraftment in patients treated with these regimens. * To determine the incidence and severity of acute and chronic graft-versus-host-disease (GVHD) in patients treated with these regimens. * To determine the survival at day 180 in patients treated with these regimens. * To determine the disease-free survival in patients treated with these regimens. * To determine the incidence of primary and secondary engraftment failure in patients treated with these regimens. * To determine the incidence of transplantation-related complications (e.g., infection, veno-occlusive disease of the liver, or organ toxicity) in these patients. * To determine the incidence of post-transplantation-related lymphoproliferative disease, secondary myelodysplastic syndromes, or other secondary malignancies in these patients. * To determine the incidence of relapse in patients treated with these regimens. * To determine post-transplantation chimerism in patients treated with these regimens. * To determine immune reconstitution in patients treated with these regimens. OUTLINE: This is a multicenter study. * Preparative regimens: Patients are assigned to 1 of 4 preparative regimens. * Regimen 1 (for patients \< 50 years of age and no contraindication to fractionated total-body irradiation (FTBI): Patients undergo FTBI 2-3 times a day on days -9 to -6 for a total of 11 fractions. Patients also receive cyclophosphamide IV over 2 hours on days -5 and -4 and fludarabine phosphate IV on days -5 to -2. * Regimen 2 (for patients \< 50 years of age and unable to tolerate FTBI due to prior dose-limiting radiotherapy or significant cardiotoxicity): Patients receive a test dose of busulfan on day -10 and then dose adjusted busulfan IV 3-4 times daily on days -9 to -6, melphalan IV on days -5 and -4, and fludarabine phosphate IV on days -5 to -2. * Regimen 3\* (for patients unable to tolerate regimen 1 or 2; no age exclusion): Patients receive fludarabine phosphate IV on days -8 to -4 and cyclophosphamide IV over 2 hours on day -3 and undergo TBI (single dose) on day -2. * Regimen 4\* (for patients unable to tolerate regimen 1 or 2): Patients receive fludarabine phosphate IV on days -7 to -3 and melphalan IV on day -2. NOTE: \*Treating physician decides the choice between regimen 3 and 4 * Umbilical cord blood (UCB) transplantation: Patients receive 2 combined units of UCB IV on day 0. Patients also receive G-CSF IV or subcutaneously beginning on day 5 (or later) and continuing until blood counts recover. * Graft-versus-host-disease prophylaxis: Patients receive cyclosporine IV twice daily beginning on day -1 followed by a taper according to institutional guidelines. Patients also receive mycophenolate mofetil orally or IV beginning on day 0 and continuing until day 27 (or as clinically indicated). After completion of study therapy, patients are followed periodically.