This phase I trial studies the side effects of capecitabine and Y-90 radioembolization in treating patients with bile duct cancer in the liver that has spread to other places in the body and cannot be removed by surgery. Radiation therapy, such as Y-90 radioembolization, injects tiny radioactive Y-90 microspheres into the blood supply next to the liver tumors to kill tumor cells. Capecitabine may make radiation more effective. Giving capecitabine and Y-90 radioembolization may work better in treating patients with bile duct cancer in the liver.