I found this glitch while messing around and looking for clues during the first part of "A Walk in Elysian Fields". The ground acts as a kind of quicksand, sucking you down under the map.
In the empty lot to the left of the destroyed home, the terrain is glitched in a number of places, causing you to hop off of and step onto ledges that aren't there. The spot in the video, I believe, is the only location where you can actually get caught in the ground and slip through it.
You don't always fall right through. Sometimes you'll shoot through the ground, sometimes you'll sink through, and sometimes you'll get stuck halfway in the ground.
You can find this location near the corner of Melrose Ave. and Hobart Blvd., near the middle of the map.