This phase III trial compares the effect immunotherapy (IO) with stereotactic body radiation therapy (SBRT) to IO alone in treating patients with liver cancer (hepatocellular cancer) that may have spread from where it first started to nearby tissue, lymph nodes, or distant parts of the body (advanced). The usual approach is treatment with IO-based drug combinations, such as atezolizumab and bevacizumab, durvalumab and tremelimumab, or ipilimumab and nivolumab. Durvalumab and tremelimumab are monoclonal antibodies that may interfere with the ability of tumor cells to grow and spread. A monoclonal antibody is a type of protein that can bind to certain targets in the body, such as molecules that cause the body to make an immune response (antigens). IO with monoclonal antibodies, such as atezolizumab, nivolumab and ipilimumab, may help the body's immune system attack the tumor, and may interfere with the ability of tumor cells to grow and spread. Bevacizumab is in a class of medications called antiangiogenic agents. It works by stopping the formation of blood vessels that bring oxygen and nutrients to tumor. This may slow the growth and spread of tumor cells. Radiation therapy uses high energy x-rays, particles, or radioactive seeds to kill cancer cells and shrink tumors. SBRT is a type of external radiation therapy that uses special equipment to position a patient and precisely deliver radiation to tumors in the body (except the brain). The total dose of radiation is divided into smaller doses given over several days. This type of radiation therapy helps spare normal tissue. Giving IO with SBRT may be more effective than IO alone in helping patients with advanced hepatocellular cancer live longer.