This phase I trial studies the side effects of genetically modified T cells and decitabine in
treating patients with recurrent or refractory epithelial or non-epithelial ovarian, primary
peritoneal, or fallopian tube cancer that has come back or has not responded to previous
treatments. White blood cells called T cells are collected via a process called
leukapheresis, genetically modified to recognize and attack tumor cells, then given back to
the patient. Decitabine may induce and increase the amount of the target protein NY-ESO-1
available on the surface of tumor cells. Giving genetically modified T cells and decitabine
may kill more tumor cells.