Alemtuzumab, Fludarabine Phosphate, and Total-Body Irradiation Followed by a Donor Stem Cell Transplant in Treating Patients With Immunodeficiency or Other Nonmalignant Inherited Disorders

Inclusion Criteria: * Primary immunodeficiency disorder or other nonmalignant inherited disease (except aplastic anemia and Fanconi anemia) treatable by allogeneic HCT * Patients with pre-existing medical conditions or other factors that renders them at high risk for regimen related toxicity or ineligible for a conventional myeloablative HCT * Donors: Related donor who is human leukocyte antigen (HLA) genotypically identical at least at one haplotype and may be genotypically or phenotypically identical for serological typing for HLA-A, B, -C, and at the allele level for -DRB1 and -DQB1; related donors must be a match or a single allele mismatch at HLA-A, B, and C (at highest resolution available at the time of donor selection) and matched at DRB1 and DQB1 by deoxyribonucleic acid (DNA) typing * Donors: Unrelated donors who are prospectively: * Matched for HLA-A, B, C, DRB1 and DQB1 by DNA typing at the highest resolution routinely available at the time of donor selection * Only a single allele disparity will be allowed for HLA-A, B, or C as defined by high resolution typing (no mismatching for DRB1 or DQB1 is allowed) Exclusion Criteria: * Patients with Aplastic anemia and Fanconi anemia * Patients with metabolic storage diseases who have severe central nervous system (CNS) involvement of disease, defined as intelligence quotient (IQ) score \< 70 * Cardiac ejection fraction \< 30% or, if unable to obtain ejection fraction, shortening fraction of \< 26%) on multi-gated…