Hi, Larry.  I believe that the show you're looking for is "Nightfall", a Canadian radio series featuring suspense and horror stories.  It was produced by the CBC from 1980 - 1983.  "All Nighter" is the title of the episode.  It's not a great one, but I hope you find it and I hope it's the story you're looking for.  The series was okay, and featured mostly Canadian actors that we're not familiar with in the U.S.