Fludarabine, Bendamustine, and Rituximab in Treating Participants With Lymphoid Cancers Undergoing Stem Cell Transplant

PRIMARY OBJECTIVES: I. To determine engraftment and dose limiting toxicity (DLT) of bendamustine in patients with lymphoid malignancies undergoing non-myeloablative allogeneic hematopoietic transplantation. SECONDARY OBJECTIVES: I. To monitor the risk of graft-versus-host disease (GVHD) and clinical responses. OUTLINE: This is a dose escalation study of bendamustine. Participants receive rituximab intravenously (IV) over 5-7 hours on days -13 and -6, fludarabine IV over 1 hour and bendamustine IV over 1 hour on days -5 to -3, and tacrolimus IV starting on day -2 and orally (PO) after hospital discharge for 6 to 8 months. Participants with matched unrelated donor (MUD) receive thymoglobulin on days -2 and -1. Participants undergo allogenic stem cell transplant over 30-45 minutes on day 0. Participants receive rituximab IV over 5-7 hours on days 1 and 8 and methotrexate IV over 30 minutes on days 1, 3, and 6. Participants with MUD also receive methotrexate IV on day 11. Participants receive filgrastim (G-CSF) subcutaneously (SC) once daily starting on day 7 until white blood cell counts recover. After completion of study treatment, participants are followed up every 3 months during year 1 and every 6 months for up to 3 years.