DISEASE CHARACTERISTICS: - Diagnosis of B-cell chronic lymphocytic leukemia or B-cell small lymphocytic lymphoma according to the International Workshop on Chronic Lymphocytic Leukemia (IWCLL) 2008 criteria - Meets 1 of the following criteria: - Early disease cohort: - Meets ≥ 1 of the following criteria: - FISH showing deletion 17p in ≥ 20% of cells (either at diagnosis or any time before study entry) either alone or in combination with other cytogenetic abnormalities - FISH showing deletion 11q in ≥ 20% of cells (either at diagnosis or any time before study entry) either alone or in combination with other cytogenetic abnormalities, unless the patient has achieved a complete remission, according to IWCLL 2008 criteria which includes CT scan, bone marrow morphology, and flow cytometry - Failed to achieve a partial response to initial purine analog-based combination therapy (e.g., fludarabine phosphate and rituximab; fludarabine phosphate, cyclophosphamide, and rituximab; pentostatin, cyclophosphamide, and rituximab; or alemtuzumab), but has no disease progression (may receive a second therapy to improve response before transplant) - Received ≥ 2 courses of induction therapy with combination therapy that is purine analog-based (e.g., fludarabine phosphate and rituximab; fludarabine phosphate, cyclophosphamide, and rituximab; or pentostatin, cyclophosphamide, and rituximab) (may not receive > 2 different regimens before proceeding to transplantation) - Stable disease or better after most recent therapy (i.e., no prior progression), according to the revised IWCLL 2008 criteria - Nodes ≤ 5 cm - Advanced disease cohort: - Meets ≥ 1 of the following criteria: - First disease progression < 24 months after completing a purine analog-based therapy (e.g., fludarabine phosphate and rituximab; fludarabine phosphate, cyclophosphamide, and rituximab; pentostatin, cyclophosphamide, and rituximab; or alemtuzumab) (this includes progression on initial therapy) - Second or subsequent progression - Stable disease or better after most recent chemotherapy, according to the revised IWCLL 2008 criteria - Nodes < 5 cm - Has an HLA-matched related or unrelated donor available - 6/6 HLA-matched related donor by low-resolution typing at HLA A, B, C, and DR - 8/8 HLA-matched unrelated donor by molecular typing at both HLA class I and class II (A, B, C, and DR loci) - No syngeneic donors PATIENT CHARACTERISTICS: - ECOG performance status 0-2 - Serum creatinine < 2 mg/dL - Calculated creatinine clearance ≥ 40 mL/min - AST < 3 times upper limit of normal - Total bilirubin < 2 mg/dL (except for patients with Gilbert syndrome) - DLCO ≥ 40% predicted - LVEF ≥ 30% by ECHO or MUGA - Not pregnant or nursing - Negative pregnancy test - Fertile patients must use effective contraception - HIV negative - Hepatitis B surface antigen negative - Anti-hepatitis B core antigen negative - Hepatitis C antibody negative - No uncontrolled diabetes mellitus or active uncontrolled serious infections PRIOR CONCURRENT THERAPY: - See Disease Characteristics - At least 4 weeks since prior cytotoxic chemotherapy or alemtuzumab