I think the term is persistence hunting (https://en.wikipedia.org/wiki/Persistence_hunting). There was an intriguing blog post years ago (which sadly I can’t find) about how terrifying a fictional portrayal of persistence hunting would be- grinding down prey through exhaustion, thinking you’ve escaped but being slowly tracked down.
Somehow that reminds of the old B-movie Surviving the Game with Ice-T.
Wooly Mammoth basically living out the plot of It Follows.
There's also the story "Go, Go, Go, Said the Bird" by Sonya Dorman in the first Dangerous Visions which is like this, in a way.