T Cell Receptor Immunotherapy Targeting HPV-16 E6 for HPV-Associated Cancers

Patients will receive Fludarabine 25 mg/m\^2/day for 5 days.

Patients will receive Cyclophosphamide 60 mg/kg/day x 2 days

On day 0, cells will be infused intravenously (IV) over 20-30 minute (between 1 and 4 days after the last dose of fludarabine)

Aldesleukin 720,000 IU/kg IV (based on total body weight) over 15 minutes approximately every 8 hours beginning within 24 hours of cell infusion and continuing for up to 5 days (maximum of 15 doses).