I'm going to give the coyotes their credit that they deserve. Coyotes have their purpose. Nobody lets their dogs run loose too many times in my area.
It depends upon who the neighbor is. If it is someone who is serious about keeping their dog confined and they had an accidental escape, I will catch the dog and return it, or crate it up to keep it safe. If it is someone who allows their dog to roam, or won't fix their fences, then the poor unfortunate dog is taking his chances.
There are 2 track greyhounds up the road who are never out. I'd catch those of I ever saw them, because their owners care. On the other hand, the local coyotes have dined on 2 Newfoundlands, 2 Boston Terriers, and a Blue Heeler in the past year. I can't protect everybody's dog, so warn them once and f they don't care enough to keep their dog home, then that's the end of it. Not the poor dog's fault that he has to die because some jerk is irresponsible.