NY-ESO-1 Specific T Cells After Cyclophosphamide in Treating Patients With Advanced Synovial Sarcoma or Myxoid/Round Cell Liposarcoma

This phase I trial studies the side effects and best way to give NY-ESO-1 specific T cells after cyclophosphamide in treating patients with advanced synovial sarcoma or myxoid/round cell liposarcoma. Placing a gene that has been created in the laboratory into white blood cells may make the body build an immune response to kill tumor cells. Drugs used in chemotherapy, such as cyclophosphamide, work in different ways to stop the growth of cancer cells, either by killing the cells or by stopping them from dividing. Giving NY-ESO-1 specific T cells with cyclophosphamide may kill more tumor cells.