This pilot clinical trial studies the side effects of pembrolizumab and radiation therapy in treating patients with stage I-III multiple myeloma that has come back after a period of improvement or that does not respond to treatment. Monoclonal antibodies, such as pembrolizumab, may block cancer growth in different ways by targeting certain cells. Radiation therapy uses high energy x-rays to kill cancer cells and shrink tumors. Giving pembrolizumab and radiation therapy may work better in treating patients with stage I-III multiple myeloma.