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 diso…