Chemotherapy, Radiation Therapy, Rituximab, and Umbilical Cord Blood Transplant in Treating Patients With B-Cell Non-Hodgkin's Lymphoma

RATIONALE: Giving low doses of chemotherapy, such as cyclophosphamide and fludarabine, total-body irradiation, and rituximab before a donor umbilical cord blood stem cell transplant helps stop the growth of cancer cells. It also stops the patient's immune system from rejecting the donor's stem cells. The donated stem cells may replace the patient's immune cells and help destroy any remaining cancer cells (graft-versus-tumor effect). Sometimes the transplanted cells from a donor can also make an immune response against the body's normal cells. Giving cyclosporine and mycophenolate mofetil after the transplant may stop this from happening. PURPOSE: This phase II trial is studying how well giving chemotherapy and radiation therapy together with rituximab and an umbilical cord blood transplant works in treating patients with B-cell non-Hodgkin's lymphoma.

OBJECTIVES: Primary * Determine the overall and event-free survival at 1 year in patients with B-cell lymphoid malignancies treated with a nonmyeloablative conditioning regimen, rituximab, and umbilical cord blood (UCB) transplantation (UCBT). Secondary * Determine the speed of neutrophil and platelet recovery post allograft in these patients. * Determine the incidence and speed of donor-derived engraftment and contribution of each UCB unit to engraftment in these patients. * Determine the incidence and severity of acute graft-vs-host disease (GVHD) at 100 days in these patients. * Determine the incidence and severity of chronic GVHD at 1 year in these patients. * Determine the incidence of serious infectious complications and correlate with laboratory measurements of immune recovery in these patients. * Determine the response to vaccination after UCBT in these patients. * Determine the incidence of treatment-related mortality at 100 days and 180 days in these patients. * Determine the incidence of malignant relapse or disease progression at 1 and 2 years in these patients. * Determine the probabilities of overall and event-free survival at 2 years after UCBT in these patients. * Determine the performance of laboratory studies investigating double-unit biology and correlate with unit engraftment in these patients. OUTLINE: * Pre-transplant rituximab therapy: Patients receive rituximab IV on days -8 or -7 and on day -4. * Nonmyeloablative conditioning regimen: Patients receive fludarabine phosphate IV over 30 minutes on days -6 to -2 and cyclophosphamide IV on day -6. Patients also undergo total-body irradiation on day -1. * Umbilical cord blood transplantation: Patients undergo umbilical cord blood transplantation on day 0. Patients receive filgrastim (G-CSF) IV or subcutaneously beginning on day 7 and continuing until blood counts recover. * Post-transplant rituximab therapy: Patients receive rituximab IV on days 7, 14, 21, and 28. * Graft-vs-host disease prophylaxis: Patients receive cyclosporine IV over 2-4 hours or orally twice daily on days -3 to 100, followed by a taper. Patients also receive mycophenolate mofetil IV or orally three times daily on days -3 to 45, followed by a taper. Treatment continues in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed periodically for 5 years. PROJECTED ACCRUAL: A total of 30 patients will be accrued for this study.