This phase II trial studies how well leflunomide, pomalidomide, and dexamethasone work for the treatment of multiple myeloma that has come back (relapsed) or does not respond to treatment (refractory). Leflunomide may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Immunotherapy with pomalidomide, may induce changes in body's immune system and may interfere with the ability of tumor cells to grow and spread. Chemotherapy drugs, such as dexamethasone, work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving leflunomide with pomalidomide and dexamethasone may work better in treating multiple myeloma compared to pomalidomide and dexamethasone alone.