In my area, there used to be a known group of wild dogs. We shot at them every chance we got!! DOC knew they were around and didn't do a whole lot about them, which in my opinion is wrong. In Illinois it is against the law for a dog to chase wildlife.
Dogs — Deer and Turkey
It is unlawful to allow your dog to chase,
harass or kill deer. Dogs may be used for
hunting except for deer and turkey.
So if a dog were to continually run deer on the property where I hunt, he would end up missing after a while.
I actually just warned a guy that lives within a quarter mile from where I hunt that his dog was chasing deer and that he might end up getting shot. He didn't even act like he cared.