It was a recurring character played by Burgess Meredith, I believe. There was another, where he was in the basement archives of a huge library, perhaps the Library Of Congress, when nuclear war broke out and destroyed everything, and apparently everyone else. Being such a bookish recluse, thick nerd glasses and all, he began to be rather happy with all the time he’d have for all those books. Then, he stumbled and broke his glasses.
Time Enough at Last. I remember feeling very sorry for Burgess Meredith's character in that one.
I think he was an employee in a store or an accountant in that one. Nobody told stories like the Twilight Zone.