I have eliminated some fox that killed some of my birds. They were mangy and stinky. Even if you eliminate both others will eventually show up. The same was for a bobcat that killed 14 birds one night I eliminated it and seen others since.
I had an issue a few years ago and spoke to a wildlife officer and he told me I could shoot if they were harming my livestock and my birds are livestock. He also mentioned they were not endangered. I have see others since.