At times you will run across a fenceline where animals are passing through but the fence is worn down from time and/or abuse.
Coyote snared in old fences will quite often damage them.
To block this type of set-up often takes a lot of time, brush and is often hard for it to look natural without it looking too "man made."
I have noticed that if blocking appears unnatural, coyotes will go around it or avoid it altogether.
The best way, I've found to do it is to to cut off a piece of woven wire fence and "ring" it right onto the old fence wire. I then cut a hole where the animals have naturally been passing through.
This of course is done during early pre-season to get the animals using it again.
I also throw in some light cut brush to help blend it in...time of course will be your best friend with that.
Animals see fence mending all the time.
While they may back off a while, they will eventually start using it again and once season opens you can set your snares in the narrow opening.
I would much prefer to have my snare fastened onto an 8 ft. 1/8th" slide (drowner) cable than fasten it onto the fence. This gets the animal away from the area, (well 8 ft. any way) and leaves the pass through open and not torn up.
Not always possible though!