when my dogs catch varmints I call it trashing.......
We have a couple dogs that we let "trash" My bulldog Tyson has caught hogs, coyote, and cattle intentionally. To date, he has never caught something that we was not released to catch.
Mandi's greyhound, Foxy, is a hog dog, but for fun, we will put her on rabbits, or other small furries.
It's only trashing, if you don't want them to do it
Heck, I bet the foundation for most of the dogs we use today, were hunting dogs... anything that would go in the pot. Hogs, coon, squirrel, etc.