That depends on what kind of critter it is and whether or not it can be legally considered "livestock". In my state there are a few game farms, and if their "stock" escape you can't shoot them. Whitetails you could get away with unless it has an obvious sign of ownership such as an ear tag, but more exotic species such as elk(Not native here) would obviously be escaped ranch critters, and therefore illegal. Feral hogs can be shot on sight here, escaped pic 'n shoot animals cannot be.