Low-Dose Total-Body Irradiation and Fludarabine Phosphate Followed by Unrelated Donor Stem Cell Transplant in Treating Patients With Fanconi Anemia

Inclusion Criteria:

* Any patient with marrow failure and increased chromosome fragility as determined in the diepoxybutane (DEB) or mitomycin C test
* Any patient with Fanconi anemia (FA) with marrow failure meeting the following criteria:
* Granulocyte count \< 0.2 x 10\^9/L
* Platelet count \< 20 x 10\^9/L
* Hemoglobin \< 8 g/dl
* Corrected reticulocyte count \<1%
* Any patient with FA as determined by DEB fragility, who has life-threatening marrow failure involving a single hematopoietic lineage
* Any patient with FA and pre-existing cytogenetic abnormality including hematopoietic malignancy (myelodysplastic syndromes \[MDS\] or acute myeloid leukemia \[AML\]) in remission
* DONOR: Unrelated Donors who are prospectively: Matched for human lymphocyte antigen (HLA)-DRB1 and DQB1 alleles (must be defined by high resolution typing); only a single allele disparity will be allowed for HLA -A, B, or C as defined by high resolution typing
* DONOR: HLA typing will be performed at the highest level of resolution available at the time of transplant

Exclusion Criteria:

* Evidence for hematopoietic malignancy in relapse
* Heart or lung disease that would prevent compliance with conditioning and GvHD regimen or would severely limit the probability of survival
* Human immunodeficiency virus (HIV) seropositive patients
* Females who are pregnant or breastfeeding, or unwilling to use contraceptive techniques during and for the 12 months following treatment
* DONOR: Donors who by DEB testing are found to have FA
* DONOR: Donors who test positive in the lymphocytotoxic crossmatch assay
* DONOR: Donors who are HIV positive
* DONOR: Donors who for other medical or psychological reasons are not suitable as donors