No Kills ever happen, unless the hounds come about a sick fox or other critter that is too weak, sick to run. The majority of animals are too quick for the hounds short legs to even get caught by them. Almost every single time when the hounds catch a scent and do get on the trail of a critter, the hounds cannot even keep up with them.
It's the law. The Hunt has the Government come and keep track of their breeding program to ensure that the pups and dogs are of regulation conformation. If the hounds are not, they are sold as pets.