Fludarabine Phosphate, Cyclophosphamide, and Total-Body Irradiation Followed by Donor Bone Marrow Transplant, Mycophenolate Mofetil, and Cyclosporine in Treating Patients With Fanconi Anemia

Inclusion Criteria: * Any patient with FA and bone marrow (BM) failure involving 2 of the following 3 lineages: granulocyte count \< 0.5 x 10\^9/L, platelet count \< 20 x 10\^9/L, or hemoglobin \< 8 g/dL * Any patient with FA who requires red blood cell or platelet transfusions because of marrow failure * Any patient with FA who has a life-threatening BM failure involving a single hematopoietic lineage * Any patient with FA and pre-existing cytogenetic abnormality including hematopoietic malignancy (acute myeloid leukemia \[AML\] or myelodysplastic syndrome \[MDS\]) in morphological remission (defined as absence of circulating blasts and bone marrow blasts \< 5% as assessed by morphology); Note that hematopoietic recovery is not required for remission status * Patients must have a negative cytotoxic cross match with donor * DONOR: Related, human leukocyte antigen (HLA)-haploidentical donors must be identical for one HLA haplotype and mismatched for any number of HLA-A, -B, -C, DRB1 or DQB1 loci of the unshared haplotype * DONOR: Unrelated, HLA-matched donors must be matched at HLA-A, B, C, DRB1 and DQB1 by deoxyribonucleic acid (DNA) typing at the highest resolution routinely available at the time of donor selection; a single allele mismatch at HLA-A, B, or C is allowed OR a single DQB1 mismatch is allowed * DONOR: Bone marrow will be the only allowed hematopoietic stem cell source * DONOR: Haploidentical donor selection will be based on standard institutional criteria, othe…