Take a look at the Hunger Royale video from another thread. Part 2, about 6 minutes in or so (just a random place I jumped to) you start to see the red border. It gets more pronounced the closer you are to death. Jump ahead to 8 minutes and you can see it progressing a bit.
Most of the time when I was playing, I didn't notice the damage border. Primarily because the damage I'd be taking would drop me to the downed state too quickly. In the Hunger Royale you had a slow life degeneration, so it made the border very obvious -- you'd be at low health for long periods of time (unless you were unlucky like me, and not only couldn't find rations but did find hostile players).