This randomized phase II trial is studying thalidomide and fludarabine to see how well they work compared to thalidomide alone in treating patients with hematologic cancer that has not responded to previous treatment with fludarabine. Thalidomide may stop the growth of hematologic cancer by stopping blood flow to the cancer. Combining thalidomide with fludarabine may increase the effectiveness of chemotherapy by making cancer cells more sensitive to the drug. It is not yet known whether thalidomide is more effective with or without fludarabine for hematologic cancer.