Heart failure is a condition in which the heart is unable to pump enough blood to the body's other organs. A heart transplant may be necessary for some individuals with end-stage heart failure. Left ventricular assist devices (LVADs) can assist the heart in pumping blood, and are commonly used until a donor heart becomes available. Bone marrow cells injected into the heart may improve heart function and may lead to earlier LVAD removal. The purpose of this study is to evaluate the safety and effectiveness of injected bone marrow cells in improving heart function in individuals with LVADs who are awaiting heart transplants.