Maybe it depends on breeding or training or something but our dog goes ballistic over coyotes and if we let him outside, I'm sure would chase. Although we've had one in the yard once and he was on a rope outside and we still managed to get him to come inside so maybe he does have some of the protective thing. But he is also terrible at accessing threats and goes crazy over deer, rabbits, squirrels, turkeys, chases all of them if he's outside. Barks at weird noises, even moving furniture around upstairs, hate HATES loud noises, terrified. Lunges at the door, barking his head off, at delivery people and guests. And recently nearly bit the vet when he never used to be bad. But I believe it's our fault, didn't relaize how protective the breed was, didn't socialize him at all, and also messed up some training and made some things worse like the vet thing. He is half Black Lab and half Great Pyrenees. But yeah basically my point is he does chase and he also used to run off. I've heard roaming is common for Pyrenees. But he does tend to sleep on the bed all day or if he's outside he will be on guard the whole time unless hes dust bathing so that's good. I think he does eventually come back too. Maybe they run it off or only go within sight or hearing of the flock then come home? If we ever get another we will take the time to properly train him and make sure he knows how to access threats, what level of aggression is necessary and when it's allowed, taught to be called off when we say so etc. Too much hassle and liability. He's a sweet sweet dog and actually usually does come when called outside and is fine once people come inside but you can't get him away from the window for anything. Well, he will back down for food or if you clip a leash though but getting a leash on can be dangerous lol we admittedly haven't worked with him very much but if you can get him away he is good and will stay put but it's getting him out of that mindset that is tricky. We didn't realize how protective they were. Just saw a cute puppy. But of course that could have been resolved with socialization and training but oh well. Sorry, I'm rambling. Are true ones supposed to stay home though?