This phase I/II trial studies the best dose and side effects of gemcitabine and how well it
works with clofarabine and busulfan and donor stem cell transplant in treating participants
with chronic lymphocytic leukemia. Drugs used in chemotherapy, such as gemcitabine,
clofarabine, and busulfan, work in different ways to stop the growth of tumor cells, either
by killing the cells, by stopping them from dividing, or by stopping them from spreading.
Giving chemotherapy before a donor stem cell transplant helps stop the growth of cells in the
bone marrow, including normal blood-forming cells (stem cells) and cancer cells. When the
healthy stem cells from a donor are infused into the patient they may help the patient's bone
marrow make stem cells, red blood cells, white blood cells, and platelets. The donated stem
cells may also replace the patient's immune cells and help destroy any remaining cancer
cells.