Low-Dose Fludarabine, Busulfan, and Anti-Thymocyte Globulin Followed By Donor Umbilical Cord Blood Transplant in Treating Patients With Advanced Hematologic Cancer

RATIONALE: Giving chemotherapy before a donor umbilical cord blood transplant helps stop both the growth of cancer cells and the patient's immune system from rejecting the donor's stem cells. When the healthy 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 chemotherapy, such as fludarabine and busulfan, and antithymocyte globulin before transplant and tacrolimus and mycophenolate mofetil after transplant may stop this from happening. PURPOSE: This clinical trial is studying how well giving low-dose fludarabine and busulfan together with anti-thymocyte globulin, followed by donor umbilical cord blood transplant works in treating patients with advanced hematologic cancer.

OBJECTIVES: Primary * Assess the feasibility of performing umbilical cord blood transplants in older patients or younger infirm patients with advanced hematologic malignancies using a reduced-intensity preparative regimen, as determined by \> 80% engraftment rate at day 180 and a \< 50% transplant-related mortality rate at day 100. Secondary * Describe the time to neutrophil and platelet recovery in patients treated with this regimen. * Determine disease-specific, event-free, and overall survival rate at days 180 and 360. * Determine the incidence, severity, and timing of acute and chronic graft-versus-host disease in patients treated with this regimen. * Evaluate T-cell, B-cell, and natural killer cell recovery in patients treated with this regimen. * Assess lineage-specific chimerism after transplantation and describe the contribution of each individual cord blood unit to post-transplantation hematopoiesis. OUTLINE: This is a pilot study. * Reduced-intensity preparative regimen: Patients receive fludarabine IV over 30 minutes on days -8 to -4, busulfan IV over 2 hours 4 times daily on days -4 and -3, and anti-thymocyte globulin IV over 6 hours on days -3 to -1. * Allogeneic umbilical cord blood transplantation: Patients undergo allogeneic umbilical cord blood transplant on day 0. Patients receive sargramostim (GM-CSF) subcutaneously or IV beginning on day 7 and continuing until blood counts recover. * Graft-versus-host disease (GVHD) prophylaxis: Patients receive tacrolimus IV continuously over 24 hours or orally (as tolerated) beginning on day -2 and continuing for approximately 9 months. Patients also receive oral mycophenolate mofetil twice daily on days 1-50. After completion of study treatment, patients are followed periodically for 2 years. PROJECTED ACCRUAL: A total of 10 patients will be accrued for this study.