I remember an episode (probably Twilight Zone) where a drunk retired actor is hired by a young producer to film a conclusion for a long ago interrupted soap opera. The producer turned out to be from an alien distant planet where our radio waves with the show just arrived and they are craving to see the conclusion. Any clues about what episode / TV show was this story about? Was it based on a short story?
Sounds like "Distant Signals" from Tales from the Darkside, an episode based on the short story of the same name by Andrew Weiner. The Futurama episode mentioned in Keen's answer seems to be based off this. Tales from the Darkside, episode 31, a summary of which is here.
Courtesy of Wikipedia:
A director is approached by a mysterious investor who asks him to complete a previous short-run and unpopular detective series called "Max Paradise", which was canceled 20 years ago before the final episodes were shown. The investor and his mysterious backers will pay any price to see the series finished, complete with bringing the original actor out of retirement. After the filming is complete, it is discovered that the investor is an alien from a planet that gets TV signals from Earth 20 years after they air. Max Paradise was popular there so he came to Earth to finish the show. Story by Andrew Weiner, adapted by Ted Gershuny and guest-starring Darren McGavin.
Possibly Futurama? In the episode When Aliens Attack, aliens who live 1000 light years away invade, after their viewing of the Fox show Single Female Laywer (an Ally McBeal parody) is interrupted. They invade, and the Planet Express crew are forced by the aliens to film a replacement for the missing episode.
If this isn't it, then this episode is certainly parodying the story you seek.
Distant Signals - an episode of Tales from the Darkside, starting Darren McGavin. Excellent, classic episode.