This phase II trial studies how well brenetafusp (IMC-F106C) works in treating patients with preferentially expressed antigen of melanoma (PRAME) positive synovial sarcoma and myxoid/round cell liposarcoma 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). Brenetafusp (IMC-F106C) is in a new class of immunotherapy called immune mobilizing monoclonal T-cell receptors against cancer (ImmTAC). Brenetafusp (IMC-F106C), may induce changes in body's immune system and may interfere with the ability of tumor cells to grow and spread.