This would never happen in the UFC, but that is only because the rings are caged octagons and not square rings with ring rope like a boxing ring.
In the fight above, check out how one fighter gets a nice leg hold around his opponent's neck and when the fight gets pushed to the edge of the ring he uses the ring rope to help choke the guy.
You gotta admit it is a pretty cool move and a great use of the environment. Okay, maybe his opponent didn't think it was very cool and neither did the ref who stopped the fight and moved the two men back into the ring.
I wonder if there is an actual rule against it or if the ref just didn't like the move?