There are plenty of shots in movies where the camera is following someone's back through a space or landscape, some are long or short. "The Evil Dead" is a good example of using a moving camera that seems to hunt or chase people down, sort of an evil spirit POV. A comedic example is when the camera follows the band members around backstage in "Spinal Tap" when they get lost and can't find the stage.
"Tree of Life" has lots of moving shots cut into semi-montages, often following people.
A lot of movies begin a character introduction by following their backs through a space, such as in the early part of "The Hunt for Red October" when you meet the Russian minister who gets the letter from Marko Ramius.
Another example of sort of a "hunting" motion is in "The Conformist" (1970) when the killers chase Dominique Sanda through the snowy woods.
There is an interesting body cam rig in the opening of "Seconds" (1966) when a character follows John Randolph through the train station.