Alemtuzumab, Fludarabine, and Busulfan Followed By Donor Stem Cell Transplant in Treating Young Patients With Hematologic Disorders

DISEASE CHARACTERISTICS: * Diagnosis of 1 of the following hematologic conditions: * Aplastic anemia with marrow aplasia, meeting all of the following criteria: * Absolute neutrophil count \< 500/mm\^3 * Platelet and/or red cell transfusion dependent * Chronic aplastic anemia, meeting all of the following criteria: * Transfusion dependent * Unresponsive to immunosuppressive therapy * Alternative matched unrelated donor has been identified * Congenital marrow failure syndrome, including any of the following (with closely matched related or unrelated donor): * Primary red cell aplasia (Diamond-Blackfan syndrome) * Congenital neutropenia (Kostmann's syndrome) * Amegakaryocytic thrombocytopenia * Congenital dyserythropoietic anemias * Other severe acquired cytopenias in which a transplantation using a combined busulfan/cyclophosphamide conditioning regimen is indicated * Hemoglobinopathy (with closely matched related or unrelated donor) * β-thalassemia major * Sickle cell anemia * Hemoglobin E/β-thalassemia * Severe immunodeficiency disease * Chediak-Higashi disease * Wiskott-Aldrich syndrome * Combined immunodeficiency disease (Nezelof's) * Hyper immunoglobulin M (IgM) syndrome * Bare lymphocyte syndrome * Chronic granulomatous disease * Familial erythrohemophagocytic lymphohistiocytosis * Other stem cell defects (e.g., osteopetrosis) * Severe immune dysregulation/autoimmune disorders * Achieved a transient response to prior immunosuppressive therapy * Chronic myelogenous leukemia * Disease in first chronic phase * Acute myeloid leukemia * Disease in first remission * Myelodysplastic syndromes * Inborn errors of metabolism * Histiocytosis * No severe combined immunodeficiency disease * Matched related or unrelated donor available by high resolution DNA typing * Related donor, meeting both of the following criteria: * Matched at both human leukocyte antigen (HLA)-Drβ1 alleles * No more than 1 mismatch at the 4 HLA-A and -B alleles * Unrelated donor, meeting 1 of the following criteria: * Marrow matched at both HLA-Drβ1 alleles AND no more than 1 mismatch at the 4 HLA-A and -B alleles * Umbilical cord blood matched at 5/6 HLA-A, -B, and -DRβ1 alleles with at least 1 -DRβ1 match AND there are ≥ 3x10\^5 CD34+ (Cluster of differentiation 34-positive) cells per kg body weight of recipient available at the time of cryopreservation PATIENT CHARACTERISTICS: * Cardiac ejection fraction ≥ 27% * Creatinine clearance ≥ 50 mL/min by 24-hour urine collection or glomerular filtration rate * DLCO (diffusion capacity of lung for carbon monoxide) ≥ 50% of predicted (corrected for anemia/lung volume) PRIOR CONCURRENT THERAPY: * No prior transplantation for leukemia from which patient remains engrafted and alemtuzumab is not needed as part of the conditioning regimen