This phase I trial is studying the side effects and best dose of alemtuzumab when given together with bendamustine hydrochloride in treating patients with relapsed chronic lymphocytic leukemia (CLL) or small lymphocytic lymphoma (SLL) that did not respond to fludarabine phosphate. Drugs used in chemotherapy, such as bendamustine hydrochloride, work in different ways to stop the growth of cancer cells, either by killing the cells or by stopping them from dividing. Monoclonal antibodies, such as alemtuzumab, can also block cancer growth in different ways. Some block the ability of cancer cells to grow and spread. Others find cancer cells and help kill them or carry cancer-killing substances to them. Giving bendamustine hydrochloride together with alemtuzumab may kill more cancer cells.