In the book, it is discovered that people can "mine for time" that then can be used to extend their own lives. However, it is discovered that the time you mine is someone else's, and you are actually taking away from their life-expectancy. Anybody familiar with it. My mom read it in high school in the mid 1980s, so it's gotta be from then or before.
Although Louis L'Amour was a western author, he was working on a series of short stories that veered from his standard (cowboys and indians) fare at the time of his death.
His daughter (Kathy L'Amour) picked up and finished that last book of short stories and I believe one of those had similarities to your inquiry.