The purpose of this study is to determine the safety of making and giving Epstein-Barr virus (EBV) immunotherapy products to subjects with nasopharyngeal carcinoma (NPC) associated with EBV that has come back or spread to other parts of the body. EBV immunotherapy product is made with white blood cells from the participants body that are collected intravenously. This EBV immunotherapy product may stop cancer cells from growing abnormally. EBV immunotherapy products have been used in several research studies for NPC. Information from these studies suggests the EBV immunotherapy products may stop the growth of NPC in some subjects.