This phase III trial compares the effect of immunotherapy (pembrolizumab) plus chemotherapy (doxorubicin) to chemotherapy (doxorubicin) alone in treating patients with dedifferentiated liposarcoma (DDLPS), undifferentiated pleomorphic sarcoma (UPS) or a related poorly differentiated sarcoma that has spread from where it first started (primary site) to other places in the body (metastatic) or that cannot be removed by surgery (unresectable). Doxorubicin is in a class of medications called anthracyclines. Doxorubicin damages the cell's deoxyribonucleic acid (DNA) and may kill tumor cells. It also blocks a certain enzyme needed for cell division and DNA repair. 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). Immunotherapy with monoclonal antibodies, such as pembrolizumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Adding immunotherapy (pembrolizumab) to the standard chemotherapy (doxorubicin) may help patients with metastatic or unresectable DDLPS, UPS or a related poorly differentiated sarcoma live longer without having disease progression.