Fludarabine Phosphate, Radiation Therapy, and Rituximab in Treating Patients Who Are Undergoing Donor Stem Cell Transplant Followed by Rituximab for High-Risk Chronic Lymphocytic Leukemia or Small Lymphocytic Lymphoma

Inclusion Criteria: * Patients with a diagnosis of CLL (or SLL) or diagnosis of CLL that progresses to prolymphocytic leukemia (PLL) * Patients with B-Cell CLL or PLL who: * Failed to meet National Cancer Institute (NCI) Working Group criteria 2 for complete or partial response after 2 cycles of therapy with regimen containing fludarabine (or another nucleoside analog, e.g. cladribine \[2-CDA\], pentostatin) or with disease relapse within 12 months after completing therapy with a fludarabine (or another nucleoside analog) containing regimen * Failed FCR or pentostatin/cyclophosphamide/rituximab (PCR) combination chemotherapy at any time point * Patients with novo or acquired "17p deletion" cytogenetic abnormality; patients should have received induction treatment but could be transplanted in 1st CR * Patients who have suitable human leukocyte antigen (HLA)-matched related or unrelated donors willing to receive filgrastim (G-CSF), undergo leukapheresis to collect peripheral blood mononuclear cell (PBMC), and to donate stem cells * RELATED DONORS: When more than one potential donor exists, priority should be given to donors based on HLA identity \> cytomegalovirus (CMV) seronegativity \> ABO compatibility \> sex matching * Donor who is HLA phenotypically or genotypically identical at the allele level at HLA-A, -B, -C, -DRB1, and -DQB1 * Must consent to G-CSF administration and leukapheresis; * Must have adequate veins for leukapheresis or agree to placement of central venous catheter (femoral, subclavian); * Only G-CSF mobilized PBMC only will be permitted as a hematopoietic stem cell (HSC) source on this protocol * UNRELATED DONORS: * Fred Hutchinson Cancer Research Center (FHCRC) matching allowed will be Grades 1.0 to 2.1; Unrelated donors who are prospectively: * Matched for HLA-A, B, C, DRB1 and DQB1 by high resolution typing * Only a single allele disparity will be allowed for HLA-A, B, or C as defined by high resolution typing * UNRELATED DONORS: Donors are excluded when preexisting immunoreactivity is identified that would jeopardize donor hematopoietic cell engraftment; this determination is based on the standard practice of the individual institution; recommended procedure for patients with 10 of 10 HLA allele level (phenotypic) match is to obtain a panel reactive antibody screens to class I and II antigens for all patients before HCT; if the PRA shows \> 10% activity, then flow cytometric or B and T cell cytotoxic cross matches should be obtained; the donor should be excluded if any of the cytotoxic cross match assays are positive; for those patients with an HLA Class I allele mismatch, flow cytometric or B and T cell cytotoxic cross matches should be obtained regardless of the PRA results; a positive anti-donor cytotoxic crossmatch is an absolute donor exclusion * UNRELATED DONORS: Patient and donor pairs homozygous at a mismatched allele in the graft rejection vector are considered a two-allele mismatch, i.e., the patient is A\*0101 and the donor is A\*0102, and this type of mismatch is not allowed * UNRELATED DONORS: Only G-CSF mobilized PBMC will be permitted as a HSC source on this protocol Exclusion Criteria: * Infection with human immunodeficiency virus (HIV) * Active diagnosis of central nervous system (CNS) involvement with CLL * Patients unwilling to use contraceptive techniques before and for 12 months after HCT * Pregnant women or females who are breastfeeding * The addition of cytotoxic agents for 'cytoreduction' with the exception of tyrosine kinase inhibitors (such as imatinib mesylate), cytokine therapy, hydroxyurea, low dose cytarabine, chlorambucil, or rituxan will not be allowed within three weeks of the initiation of conditioning * Active bacterial or fungal infections unresponsive to medical therapy * Performance status: Karnofsky score \< 60 for adult patients * Cardiac ejection fraction \< 40%; ejection fraction is required if age \> 50 years or there is a history of prior transplant, anthracycline exposure or history of cardiac disease; and poorly controlled hypertension despite multiple antihypertensives * Diffusing capacity of the lung for carbon monoxide (DLCO) \< 40%, total lung capacity (TLC) \< 40%, forced expiratory volume in 1 second (FEV1) \< 40% and/or requiring continuous supplementary oxygen, or severe deficits in pulmonary function testing as defined by pulmonary consultant service; and the FHCRC principal investigator (PI) of the study must approve of enrollment of all patients with pulmonary nodules * Patients with clinical or laboratory evidence of liver disease would be evaluated for the cause of liver disease, its clinical severity in terms of liver function, and the degree of portal hypertension; patients will be excluded if they are found to have fulminant liver failure, cirrhosis of the liver with evidence of portal hypertension, hepatic damage with bridging fibrosis, alcoholic hepatitis, esophageal varices, a history of bleeding esophageal varices or hepatic encephalopathy, uncorrectable hepatic synthetic dysfunction evidenced by prolongation of the prothrombin time, ascites related to portal hypertension, bacterial or fungal liver abscess, biliary obstruction, chronic viral hepatitis with total serum bilirubin \> 3 mg/dl, or symptomatic biliary disease * Patients with active non-hematologic malignancies (except non-melanoma skin cancers); this exclusion does not apply to patients with non-hematologic malignancies that do not require therapy * Patients with a history of non-hematologic malignancies (except non-melanoma skin cancers) currently in a complete remission, who are less than 5 years from the time of complete remission, and have a \> 20% risk of disease recurrence; this exclusion does not apply to patients with non-hematologic malignancies that do not require therapy * DONOR: Age \< 12 years * DONOR: Identical twin * DONOR: Pregnancy * DONOR: Infection with HIV * DONOR: Inability to achieve adequate venous access * DONOR: Known allergy to filgrastim (G-CSF) * DONOR: Current serious systemic illness