Fludarabine Phosphate, Rituximab, and Bevacizumab in Treating Patients With B-Cell Chronic Lymphocytic Leukemia That Has Relapsed or Not Responded To Treatment

RATIONALE: Drugs used in chemotherapy, such as fludarabine phosphate, 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 rituximab and bevacizumab, can 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 fludarabine phosphate together with rituximab and bevacizumab may kill more cancer cells. PURPOSE: This phase II trial is studying how well giving fludarabine phosphate together with rituximab and bevacizumab works in treating patients with B-cell chronic lymphocytic leukemia that has relapsed or not responded to treatment.