This phase II trial studies how well stereotactic body radiotherapy and ipilimumab work in treating patients with stage IV melanoma. Stereotactic body radiotherapy (SBRT) may be able to send x-rays directly to the tumor and cause less damage to normal tissue. Monoclonal antibodies, such as ipilimumab, target certain cells to interfere with the ability of tumor cells to grow and spread. Giving SBRT with ipilimumab may kill more tumor cells.