Most ornithologists believe feral cats to be the #2 cause of song bird decline in North America and I am sure they are high up there for game birds well. In VA it is illegal to shoot a cat or dog, even if they are lose on your property! The only way you can legally shoot a dog is if it is an immediate threat to you or your property. With cats as dogs, SSS often applies but be careful of states laws. They all vary...
Here in VA in many counties it is legal to hunt deer with dogs and during firearms season, you will often have packs of deer hounds running around your land. Many are have collars, some even have tattoos and GPS units on them. They are usually the more valuable dogs that are worth a darn. Many of the dogs just go along to make noise. At the end of the season you will see many thin mangy dogs running around as the hunt clubs don't seem to care much for them. It is a shame!