Combination Chemotherapy Followed by Donor Stem Cell Transplant in Treating Patients With Relapsed or High-Risk Primary Refractory Hodgkin Lymphoma

DISEASE CHARACTERISTICS: * Histologically confirmed classical Hodgkin lymphoma, including CD20+ disease * No lymphocyte predominant histology * Primary refractory or relapsed disease with all 3 risk factors, failed platinum-based chemotherapy, or disease relapsed more than 100 days after autologous stem cell transplantation, proven by biopsy or fine-needle aspiration (cytology) of an involved site * Risk factors are defined as B-symptoms, extranodal sites of disease, and disease remission lasting \< 1 year after first-line therapy * Failed doxorubicin hydrochloride or mechlorethamine hydrochloride-containing front-line therapy * Fludeoxyglucose F 18-PET scan demonstrating PET-avid disease * No more than 2 prior salvage chemotherapy regimens (for patients proceed to allogeneic hematopoietic stem cell transplantation \[AHSCT\]) * Donor available meeting 1 of the following criteria (for patients proceed to AHSCT): * HLA-matched or one allele mismatched related donor * Genotypically or phenotypically matched at ≥ 9/10 of the A, B, C, DRB1, and DQB1 loci, as tested by high resolution * Peripheral blood stem cells (PBSC) collected * HLA-matched unrelated donor * Matched at ≥ 9/10 (allele mismatch only) of the A, B, C, DRB1, and DQB1 loci, as tested by high resolution * PBSC or bone marrow collected * Umbilical cord blood (2 units) * must be ≥ 4/6 HLA-A, B antigen, and DRB1 allele matched with recipient PATIENT CHARACTERISTICS: * Platelet count…