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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.

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I think this is Niven's A World Out of Time

The group pauses near some ruins, and the protagonist tries to hide from the slavers inside a cabinet/closet he finds in the ruins.

In the story, Corbell escapes the woman enslaving him, and enters a teleport booth, and attempts to use that to escape, but fails.

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.

Corbell feels stronger, and realizes he has somehow found a Fountain of Youth - but he doesn't know what did it, until he experiments with several different ideas. The answer is:

The teleport booth actually teleports out of each cell the components that are the result of aging. These removed metabolic poisons form a fine dust that Corbell sees but doesn't initially understand.

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    I agree, World out of Time. Commented Jul 12, 2022 at 23:39
  • 7
    Amazing, helpful answers in just a few minutes. I've just put in an order for used paperbacks of: "A World Out Of Time," "The Integral Trees," and "The Smoke Ring." Many thanks, again, for all the help.
    – Mario
    Commented Jul 12, 2022 at 23:57
  • I'm very happy to help
    – Andrew
    Commented Jul 13, 2022 at 1:21
  • I just made an slight edit to your spoiler to correct the unaging process.
    – DoxyLover
    Commented Jul 13, 2022 at 13:40

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