Brief Summary: The purpose of this study is to evaluate the safety of progressively substituting day +3 and +4 post-transplant cyclophosphamide (PT-CY) with post-transplant bendamustine (PT-BEN) in myeloablative (MAC) haploidentical hematopoietic cell transplantation (HHCT) for patients with hematological malignancies. The goal of the Phase 1 component of the study is to evaluate the safety of progressively substituting post-transplant cyclophosphamide (PT-CY) given on Days +3 and +4 with bendamustine (PT-BEN). The Phase I component of the study has been completed. The Phase Ib component of the study will continue to evaluate the safety and efficacy of subjects who receive PT-BEN on Days +3 and +4 at the maximum tolerated dose determined by Phase I. The Phase Ib component of the study has been completed. Approximately, 18-36 subjects will be treated as part of Phase I and 15 as part of Phase Ib. Approximately 18 subjects will be used as controls, subjects that receive no PET-BEN, for direct comparison. Total, approximately 38-56 treatment and control patients and 38-56 donor subjects will be enrolled.

Detailed Description: This study will follow the standard-of-care bone marrow transplant (BMT), with the only exception being to progressively substitute post-transplant cyclophosphamide (on Days +3 and +4 after BMT) with bendamustine. Six dose levels were planned for the Phase I component of the study, consisting of a combination of sequentially reduced doses of cyclophosphamide (PT-CY) and increased doses of bendamustine (PT-BEN) initially on Day +4 after BMT, followed by the same sequential reduction and increase on Day +3. An interim analysis was performed after cohort 3 was completed in Phase I and included a preliminary comparison between treatment and control groups. Phase Ib will evaluate patients treated with PT-CY on day +3 and PT-BEN on day +4. Control patients will be patients that have declined to participate in the main trial but will receive haploidentical BMT with the current standard of two days of PT-CY (and no PT-BEN) and will be consented for the immune monitoring studies only.