Reduced Intensity Donor Stem Cell Transplant in Treating Patients With High Risk Acute Lymphocytic Leukemia in Complete Remission

Inclusion Criteria: * ADULT PATIENTS: * Patients 50-75 years old with high risk ALL in first CR (CR1) or ALL in CR \>= second CR (CR2) * Patients \>= 18 years old and \< 50 years old with high risk ALL in CR1 who are not eligible for a conventional allogeneic transplantation based on general medical condition * Patients \>= 18 years old and \< 50 years old with high risk ALL in CR1 who refuse a conventional allogeneic transplant * Patients \>= 18 years old and \< 50 years old with ALL in CR \>= CR2 who are not eligible for a conventional allogeneic transplantation based on general medical condition * Patients \>= 18 years old and \< 50 years old with high risk ALL in CR \>= CR2 who refuse a conventional allogeneic transplant * CR is defined as \< 5% blasts by morphology on a bone marrow aspirate and the absence of peripheral blasts * High risk adult ALL in CR1 includes those patients with one or more of the following: * Age \>=30 years * Non T-cell phenotype * Cytogenetic abnormalities including t(9;22), t(4;11), trisomy 8, or monosomy 7 * Failure to achieve CR after 4 weeks of induction chemotherapy * PEDIATRIC PATIENTS: * Patients \< 18 years old with ALL in high risk CR1 who are not candidates for conventional allogeneic transplantation based on general medical condition * Patients \< 18 years old with ALL in CR \>= CR2 who are not candidates for conventional allogeneic transplantation based on general medical condition * Patients \< 12 years old require approval by the Fred Hutchinson Cancer Research Center (FHCRC) principal investigator prior to enrollment * CR is defined as \< 5% blasts by morphology on a bone marrow aspirate and absence of peripheral blasts * High risk pediatric ALL in CR1 includes those patients with one or more of the following: * Cytogenetic abnormalities including: * t(9;22) with a white blood cell (WBC) \>= 25,000 at diagnosis or * t(4;11) in patients \< 1 year old and \>= 10 years old or * Hypodiploidy (\< 45 chromosomes) * Failure to achieve CR after 4 weeks of induction chemotherapy * Persistent peripheral blasts after one week of induction chemotherapy * DONOR: FHCRC matching Grade 2.1: Unrelated donors who are prospectively: * Matched for human leukocyte antigen (HLA)-DRB1 and DQB1 alleles (must be defined by high resolution typing) and * Only a single allele disparity will be allowed for HLA-A, B, or C as defined by high resolution typing * DONOR: A positive anti-donor cytotoxic crossmatch is an absolute donor exclusion; 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; the recommended procedure for patients with 10 of 10 HLA allele level (phenotypic) match is to obtain a panel reactive antibody (PRA) screens to class I and class II antigens for all patients before hematopoietic cell transplantation (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 * DONOR: Patient and donor pairs homozygous at a mismatched allele 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 * DONOR: Donor must consent to peripheral blood stem cell (PBSC) mobilization with filgrastim (G-CSF) arranged through the National Marrow Donor Program (NMDP) or other donor centers Exclusion Criteria: * Active central nervous system (CNS) disease * Presence of circulating leukemic blasts (in the peripheral blood) detected by standard pathology * Fertile men or women unwilling to use contraceptive techniques during and for 12 months following treatment * Pregnancy or breastfeeding * Human immunodeficiency virus (HIV) seropositivity * ORGAN DYSFUNCTION, ADULT CRITERIA: * Requiring supplementary continuous oxygen OR diffusing capacity of the lung for carbon monoxide (DLCO) \< 40% * Cardiac ejection fraction \< 35% * 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, alcoholic hepatitis, esophageal varices, a history of bleeding esophageal varices, hepatic encephalopathy, uncorrectable hepatic synthetic dysfunction evinced by prolongation of the prothrombin time, ascites related to portal hypertension, bridging fibrosis, bacterial or fungal liver abscess, biliary obstruction, chronic viral hepatitis with total serum bilirubin \> 3 mg/dL, and symptomatic biliary disease * Karnofsky performance score \< 50 * ORGAN DYSFUNCTION, PEDIATRIC CRITERIA: * Lansky play-performance score \< 40 * Patients with active non-hematologic malignancies (except non-melanoma skin cancers) * 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