An old, white haired, tired-of-life man is taken prisoner and force-marched across the landscape as part of a chain-gang of slaves. The group pauses near some ruins, and the protagonist tries to hide from the slavers inside a cabinet/closet he finds in the ruins. He is recaptured, but over the course of the next few days notices that he feels stronger and is no longer struggling to keep up with the group. One of the slavers rips out a handful of hair from the old man's head, shows him the mostly white hair with dark roots, and accuses him of finding the Fountain of Youth.
This cabinet/closet seems like a nearly instantaneous version of Heinlein's Howard Families rejuvenation, or Niven's Autodoc, but I don't think the protagonist is either Lazarus Long or Carlos Wu.
I can't remember the length of the story, but probably a novella or a full novel -- from the 1970's or 1980's.