Bortezomib and Chemotherapy in Treating Participants With Lymphoid Malignancies Undergoing Stem Cell Transplant

Inclusion Criteria: * Any histological subtype of CD20+ lymphoid malignancies or T-cell lymphoid malignancies. * Patients with CD20+ lymphoid malignancies in relapse after failing \>= 1 prior regimen of conventional treatment and not eligible for non-myeloablative transplant. Patients with T-cell lymphoid malignancies can either be in relapse or newly diagnosed with high risk features (such as high International Prognostic Index \[IPI\] of \>= 2). * Patients with prior non-myeloablative transplant are eligible if not from the same donor. * A fully-matched or one-antigen mismatched sibling or unrelated donor. * Left ventricular ejection fraction (EF) \>= 40% with no uncontrolled arrhythmias or symptomatic heart disease. * Forced expiratory volume in one second (FEV1), forced vital capacity (FVC) and diffusion capacity of the lung for carbon monoxide (DLCO) \>= 40%. * Serum creatinine \< 1.8 mg/dL. * Serum bilirubin \< 3 X upper limit of normal. * Serum glutamate pyruvate transaminase (SGPT) \< 3 X upper limit of normal. * Voluntary signed, written Institutional Review Board (IRB)-approved informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care. * Men and women of reproductive potential must agree to follow accepted birth control methods for the duration of the study. Female subject is either post-menopausal or sur…