This phase II trial studies how well atezolizumab, cobimetinib, and eribulin work in treating patients with inflammatory breast cancer that has spread to other places in the body (metastatic). Immunotherapy with monoclonal antibodies, such as atezolizumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Cobimetinib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as eribulin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving atezolizumab, cobimetinib, and eribulin may work better in treating patients with inflammatory breast cancer.