This pilot, phase I trial studies the safety of cancer-testis antigen (NY-ESO-1)-specific T cells (a type of immune cell) in treating patients with NY-ESO-1-expressing sarcomas that have spread to other places in the body and are receiving palliative (relief of symptoms and suffering caused by cancer) radiation therapy. Placing a modified gene for NY-ESO-1 into white blood cells may help the body build an immune response to kill tumor cells that express NY-ESO-1. Palliative radiation therapy may help patients with advanced sarcoma live more comfortably. Giving NY-ESO-1-specific T cells following palliative radiation therapy may be a better treatment for patients with sarcomas.