Just to add my experience to the equation from having trailed with dogs quite a few wounded animals, there is no "usually" with wounded animals. Sometimes they act like they were never hit, sometimes they run straight the direction they were facing, sometimes they wheel and go back the way they were coming from, and they will jump a fence with their dying heartbeat. I've recovered deer within feet of a fence they just jumped, and have found literally feet of gut hung on a top strand of wire. Some go to water, some gain elevation, some bed multiple times, some bed only a final time. Whatever you've heard about what a wounded animal will do, forget it, I've probably seen them do the opposite.
Just something to keep in mind when considering shooting near a property line.
Just something to keep in mind when considering shooting near a property line.