Cytoxan, Fludara, and Antithymocyte Globulin Conditioning Followed By Stem Cell Transplant in Treating Fanconi Anemia

30 mg/kg/day will be administered after MP on days -6, -5, -4, -3 and -2.

5 mg/kg is to be given as a 2 hour infusion, Days -6 through -3.

35 mg/m\^2 intravenously (IV) on days -6 through -2.

Bone marrow or umbilical cord blood infusion on day 0.

Methylprednisolone (MP) 2 mg/kg/day intravenously every 24 hours will be given from day -6 until day -2 as a premedication for ATG.

5 mcg/kg per day intravenously (IV) continue until Absolute neutrophil count \> or = 2.5 x 10\^9/L

Cyclosporine IV over 2 hours or orally every 8-12 hours beginning on day -3 and continuing until day 100, followed by a taper.

Day -3 through day +30 or for 7 days after engraftment, whichever day is later, if no acute GVHD. Engraftment is defined as 1st day of 3 consecutive days of absolute neutrophil count \[ANC\] \> 0.5 x 10\^9/L. MMF will be given at a dose of 15 mg/kg/dose every 8 hours PO (to a maximum dose of 1 gram).