Donor Stem Cell Transplant With Treosulfan, Fludarabine, and Thiotepa in Treating Patients With Non-malignant Disorders

Inclusion Criteria: * Patient with nonmalignant disease treatable by allogeneic HCT * Patient with a nonmalignant disease that is not clearly defined (a patient with a non-malignant disease for whom genetic testing has been done and a genetic mutation responsible for their non-malignant disease phenotype has not been identified) are eligible for the study following discussion with and approval by the protocol principal investigator (PI) (Dr. Lauri Burroughs) * Age \< 50 years * DONOR: Human leukocyte antigen (HLA)-identical related donor OR unrelated donor matched for HLA-A, B, C, DRB1 and DQB1 or mismatched for a single allele at HLA-A, B, C, or a single DQB1 antigen or allele mismatch by high resolution deoxyribonucleic acid (DNA) typing * DONOR: Bone marrow is the preferred cell source (when feasible). However, peripheral blood stem cells (PBSC) is also allowed and the PI may determine if PBSC is preferred for certain patients * The recommended total nucleated cell count (TNC) for bone marrow grafts is \>= 4.0 x 10\^8 TNC/kg (actual recipient weight) * The recommended CD34 cell count for PBSC grafts is \>= 5 x 10\^6 CD34/kg (actual recipient weight) and the recommended maximum CD34 cell count for PBSC grafts is 10 x 10\^6 CD34/kg (actual recipient weight) * DONOR: HLA-matched sibling bone marrow in combination with HLA-matched sibling umbilical cord blood if the HLA-matched sibling umbilical cord blood was collected and stored. The HLA-matched sibling bone marrow and cord blood would be matched for HLA-A, B, C, DRB1 and DQB1 Exclusion Criteria: * Patients with idiopathic aplastic anemia and Fanconi anemia; patients with aplastic anemia associated with paroxysmal nocturnal hemoglobinuria (PNH) or inherited marrow failure syndromes (except Fanconi anemia) will be allowed * Impaired cardiac function as evidenced by ejection fraction \< 35% (or, if unable to obtain ejection fraction, shortening fraction of \< 26%) or cardiac insufficiency requiring treatment or symptomatic coronary artery disease. Patients with a shortening fraction of \< 26% may be enrolled if approved by a cardiologist * Impaired pulmonary function as evidenced by carbon monoxide diffusing capability (DLCO) corrected \< 50% of predicted (or, if unable to perform pulmonary function tests, then oxygen \[O2\] saturation \< 92% on room air) * Impaired renal function as evidenced by: * Estimated creatinine clearance \< 60 mL/min/1.73m\^2 using either the Chronic Kidney Disease Epidemiology Collaboration (CKD EPI) equation for adult patients (\>= 18 years old), or the updated Schwartz formula for pediatric patients (\< 18 years old). If the estimated creatinine clearance is \< 60 mL/min/1.73m\^2, then renal function must be measured by 24-hour creatinine clearance, Iothalamate, Iohexol or nuclear GFR and the patient is excluded if their measured creatinine clearance is \< 50 mL/min/1.73 m\^2, OR * Serum creatinine \> 2 x upper limit of normal, OR * Dialysis dependent * Evidence of synthetic dysfunction or severe cirrhosis requiring deferral of conditioning as recommended by a gastroenterology specialist * Active infectious disease requiring deferral of conditioning as recommended by an infectious disease specialist * Positive for HIV (human immunodeficiency virus) * Females who are pregnant or breast-feeding * Known hypersensitivity to treosulfan, fludarabine, and/or thiotepa * DONOR: Donors deemed unable to undergo marrow harvesting of PBSC mobilization and leukapheresis * DONOR: HIV-positive donors * DONOR: Donors with active infectious hepatitis * DONOR: Female donor with positive pregnancy test * DONOR: Donors are excluded if the patient has an identified antibody against a donor-specific HLA locus as specified in standard practice * DONOR: HLA-matched sibling cord blood units that have not passed donor screening for infectious disease markers as recommended by the National Marrow Donor Project (NMDP) will not be used unless a waiver is signed by the clinical attending allowing use of cord blood unit. Cord blood units are presumed to be cytomegalovirus (CMV) negative regardless of serologic testing due to passive transmission of maternal CMV antibodies