The Outer Limits - Season 2 Episode 19 Falling Star

Pop singer Melissa McCammon is about to commit suicide. With her once meteoric career at a standstill and her husband cheating on her, she sees no hope. Then she encounters Rachael, an ardent fan from the future. Rachael is a time traveler -- and an uninvited tourist in Melissa's body. She persuades Melissa to give life a second chance, but in the process, she changes history. Now, authorities from the future want Melissa dead and will resort to anything -- including murder -- to preserve their version of the past.