I have found a few deer, or what was left of them, caught in fences over the years, maybe one every 3 or 4 years I would say. Years ago a friend and I found a young deer, still very much alive, that was caught in a fence like the one Shedhunter1 showed. We tried to get him free by pulling him out, but that wasn't going anywhere. So we grabbed him and flipped up and back over the fence and voila, he was free.
I also shot a deer on my farm once that had been caught in the neighbors fence. I happened upon a nice sized doe during the shotgun season that tried to get up and run, but it couldn't get up on its' feet and run. It kind of snowplowed all over the place and was making quite a racket. I then noticed that it was missing its' two front legs...bummer! I shot it to put it out of its' misery and then traced it back to find where it caught both front legs in the top of a cattle panel and then had struggled until it basically tore both feet off and then rolled/plowed its' way downhill to where I found it.
The places where I have found deer caught in fences have almost always been strong, cattle-tested fences that are maybe a bit taller than the norm. In most cases, a back leg, or sometimes both, goes through the fence just below the top wire and then the deer, or what is left of it, is on the other side.