Boy I hate to see that, he’s in for a rough time with that wound.
That said, I have seen a few 3 legged coyotes in my years of predator hunting.
All of them were missing front legs though and they all seemed quite healthy and lived productive lives up to the point they were taken.
That backleg on the above pictured deer is extremely bad and will probably mean his demise.
I shot this hog several years ago and it had a severe wound to its lower jaw.
It appears that someone tried for a head shot (or had the lead wrong on a running shot) and snapped a round through its lower jaw breaking it, knocking out teeth on both sides of the jaw and severing the tongue.
When I shot him I was standing on the dam (high side) of a stock tank and he was knee deep in the tank bobbing his head up and down in water trying to drink with that big a$$ed hole in his jaw.
I was about 50 yards away and could see he was skinny and all drawn up but I couldn’t see the wound in his jaw but I knew there was something “wrong” with him.
I eyeballed him for a few minutes through the 2x scope on my rifle and finally decided whatever was wrong with him, he had to go.
I sent a 300 grain .458 diameter JHP right between his eyes and put him out of his misery.
When I walked up on him he stank all to be damned (much worse than your standard wild pig stink) as all that mortified tissue in his face had turned exceptionally bad.
I drug him out of the tank and left him to feed the coyotes and the buzzards as the infection (in my mind) had left what little meat was left on him spoiled.
I fear that deer is in for very hard and miserable time with his leg and that is too bad.