happened to me
I "lost" my first deer( age 14) to this very situation in a crowded north eastern state w/ to many hunters and not enough space!!! I was pretty bummed out. Despite that apparent mortality of the hit, the "rule" of the woods was the guy who put it down got the deer. Darn guy should have given that deer to a kid (me) though!
I decided long ago that I did not want a deer that somebody else had put a hole in, though one could make a plausible argument about busted legs and stopping a cripple that would otherwise escape to rot. I'd give up such a deer in a heartbeat if a guy showed up trailing it.
Fortunately, I changed venues long ago and have not faced the situation again.