Study of Palifermin (Kepivance) in Persons Undergoing Unrelated Donor Allogeneic Hematopoietic Cell Transplantation

Background: \- In allogeneic stem cell transplantation (SCT), stem cells are taken from a donor and given to a recipient. Sometimes the recipient's immune system destroys the donors' cells. Or donor immune cells attack the recipient's tissues, called graft-versus-host disease (GVHD). This is less likely when the recipient and donor have similar human leukocyte antigens (HLA). Researchers want to see if the drug palifermin improves the results of allogeneic SCT from HLA-matched unrelated donors. Objective: \- To see if high doses of palifermin before chemotherapy are safe, prevent chronic GVHD, and improve immune function after transplant. Eligibility: \- Adults 18 years of age or older with blood or bone marrow cancer with no HLA-matched sibling donor, but with a HLA-matched unrelated donor. Description of Research Study: * Participants will be screened with medical history, physical exam, and blood and urine tests. They will have scans and heart and lung exams. * Before transplant, participants will: * Have many tests and exams. These include blood tests throughout the study and bone marrow biopsy. * Get a central line catheter if they do not have one. * Have 1-3 rounds of chemotherapy. * Have more tests to make sure they can have the transplant, including medical history, physical exam, blood tests, disease specific restaging. * Get palifermin by intravenous (IV) and conditioning chemotherapy to prepare for hematopoietic stem cell transplantation (HSCT). They will get other drugs; some they will take at least 6 months. * Participants will get the HSCT. * After transplant, participants will: * Be hospitalized at least 3-4 weeks. * Monitored at least weekly for the first 100 days. * Stay near District of Columbia (D.C). for approximately 100 days post-transplant. * After 100 days post-transplant - visit National Institutes of Health (NIH) 5 times the first 2 years, then yearly until 5 years post-transplant. * Additional tests/procedures may be performed to monitor safety, response to transplant, side effects.