IMO

Hunting scenario (in order to hunt and get the animal not just to kill it)

If we assume that “appropriate” bullet is used - as soon as I can’t achieve a full chest cave penetration behind the shoulders on a perfect broadside standing animal every time (assuming there is a clear shot present without any obstacles).

Defending scenario (one must take a shot at all cost, right there right now)

If we assume that “appropriate” bullet is used - as soon as I can’t achieve a full brain cavity penetration at any angle on headshots and break a spine at any angle anywhere along its length on spine shots.

Of course this is theory and I might change my mind just now