• Overall survival at 180 days from the time of transplant [ Time Frame: Measured at Month 6 and Year 1 ] [ Designated as safety issue: No ]
  

• Neutrophil recovery [ Time Frame: Measured at Day 28 ] [ Designated as safety issue: No ]
  
• Primary graft failure [ Time Frame: Measured at Day 56 ] [ Designated as safety issue: Yes ]
  
• Secondary graft failure [ Time Frame: Measured at Day 100 ] [ Designated as safety issue: Yes ]
  
• Platelet recovery [ Time Frame: Measured at Days 100 and 180 ] [ Designated as safety issue: No ]
  
• Donor cell engraftment [ Time Frame: Measured at Day 56 ] [ Designated as safety issue: No ]
  
• Acute graft-versus-host disease (GVHD) [ Time Frame: Measured at Day 100 ] [ Designated as safety issue: No ]
  
• Chronic GVHD [ Time Frame: Measured at Year 1 ] [ Designated as safety issue: No ]
  
• Progression-free survival [ Time Frame: Measured at Year 1 ] [ Designated as safety issue: No ]
  
• Treatment-related mortality (TRM) [ Time Frame: Measured at Day 100 ] [ Designated as safety issue: Yes ]
  
• Infections [ Time Frame: Measured at Year 1 ] [ Designated as safety issue: No ]
  

Leukemia and lymphoma are types of blood cancers. Chemotherapy is a common treatment option for people with these types of cancers, but if the cancer does not respond well to chemotherapy, or if the cancer returns, a bone marrow transplant is another treatment option. In a bone marrow transplant procedure, healthy bone marrow is taken from a donor and transplanted into the patient. Bone marrow can be donated by a family member or an unrelated donor who has a similar type of bone marrow. Most bone marrow transplants are performed using a donor who is a perfect or close-to-perfect tissue match. However, for participants in this study, researchers have determined that a completely matched donor is unavailable within participants' families, and an unrelated donor match has not been found either. Participants do, however, have a family member who is a partial tissue match.

Typically, people who are undergoing a bone marrow transplant receive high doses of chemotherapy before the transplant to prepare their bodies to accept the donor bone marrow. In this study, participants will undergo a new type of bone marrow transplant called a nonmyeloablative transplant, which is a reduced intensity method of transplantation that does not require high doses of chemotherapy. The purpose of the study is to examine the safety and effectiveness of a nonmyeloablative bone marrow transplant that uses partially matched bone marrow donated by a family member as a treatment option for people with leukemia or lymphoma.

This study will enroll people with leukemia or lymphoma who have a family member with a partial tissue match.

Participants will be admitted to the hospital and will first receive a type of chemotherapy called fludarabine, which will be given intravenously for 5 days. In addition, another type of chemotherapy, cyclophosphamide, will be given intravenously on the first and second day. After 5 days, participants will receive a small dose of radiation. The next day, participants will undergo the bone marrow transplant. The third and fourth day after the transplant, participants will receive high doses of cyclophosphamide to help prevent two complications, graft rejection, which occurs when the body's immune system rejects the donor bone marrow, and graft-versus-host disease (GVHD), which is an attack by the donor cells on the body's normal tissues. On the fifth day after the transplant, participants will receive two additional medications, tacrolimus and mycophenolate mofetil (MMF), to help prevent GVHD; some participants may receive cyclosporine instead of tacrolimus. Participants will receive MMF for about 5 weeks and tacrolimus for about 6 months. Also beginning on the fifth day after the transplant, participants will receive daily injections of a growth factor called granulocyte-colony stimulating factor (G-CSF), which is a natural protein that increases the white blood cell count; G-CSF will be continued until a participant's white blood cell count is normal again.

Participants will remain in the hospital for approximately 2 to 3 months, but possibly longer if there are complications. While participants are in the hospital, blood samples will be collected regularly to evaluate the response and possible side effects to treatment, including GVHD. If necessary, participants will receive platelet and red blood cell transfusions. Follow-up study visits will occur 6 months and 1 year after the transplant. At Months 1, 2, 6, and 12 after the transplant, blood or bone marrow samples will be obtained. Study researchers will keep track of participants' medical condition through phone calls or mailings to participants and their doctors once a year for the rest of the participants' lives.