The Twilight Zone (1985)

A modern-day miner has an argument with his wife and then goes off to work in the local mine. A collapse traps him, but he finds another survivor - a miner who claims to be from 1912. The two men figure out that somehow they have become connected through time. The modern-day man helps the 1912 miner to survive, and the latter is rescued. The modern-day miner appears trapped...but the rescuers look in an unexpected spot and find him. It turns out the 1912 miner wrote a letter marked for delivery 74 years later directing them where to search.