Genetically Modified T Cells and Decitabine in Treating Patients With Recurrent or Refractory Ovarian, Primary Peritoneal, or Fallopian Tube Cancer

Inclusion Criteria: * Patients with recurrent or refractory epithelial or non-epithelial ovarian, primary peritoneal or fallopian tube carcinoma who have received platinum containing chemotherapy and either has platinum refractory or resistant disease, or if plantinum sensitive disease, have received \>= 2 lines of chemotherapy. Subjects may have received PARP inhibitators , bevacizumab or immunotherapy. Non-epithelial tumors of the ovary include sarcomas, granulosa cell tumors and malignant germ cell tumors including chiriocarcinoma * Have been informed of other treatment options * Must be HLA- A\*02;01 positive; retesting is not required for patients who have previous documented HLA-A\*02;01 positivity * Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Life expectancy of \> 4 months * At least 4 weeks from prior chemotherapy, radiotherapy or immunotherapy, or prior investigational agents * Must have measurable disease as defined by irRECIST * Must have adequate venous access for apheresis; (pheresis catheter placement for cell collection is allowed) * Women of childbearing potential in agreement to use acceptable birth control methods for the duration of the study and until persistence of the study drug is no longer detected in the peripheral blood; this may be a period of several years; methods for acceptable birth control include: condoms, diaphragm or cervical cap with spermicide, intrauterine device, and hormonal contraception; it is rec…