My Pyrenees live with the sheep and sleep with the sheep in their shelters and run-ins—so they are inside the fence with the sheep. This protects the Pyrs both from vehicles, etc. but also from themselves, as without being given a boundary, they would be tempted to take on the whole neighborhood or county as their responsibility to protect. I have heard folks say that their LGDs may leave the fenced area if they are chasing a predator but then always come back, but I have not had this happen (yet).
My fencing is mostly 5-strand high-tensile electric, with the "winter" yard near the barn being a combination of high tensile, livestock panels, and woven wire. I have one field beyond my current pasture that I'm hoping to fence where I will probably use a combination of woven wire with one high-tensile wire run above it, and one run on the inside at 30 inches to keep the sheep off the fence. It is tempting to put a strand of barbed wire on the outside (1-2 inches above soil) to keep predators from digging, but I'm not sure whether I will or not. I also use Premier's ElectroNet or TensionNet to subdivide the pasture.
The Pyrenees respect the electric fences very well—the only time I've had one go through or under a fence was with my old Lady, who absolutely loved my granddaughter and would do it to go to her. When Katie got older, Lady still loved her but seemed less worried about her and stopped doing that. My dogs will bark at cars, trucks and tractors passing on the road because they are so territorial and believe nothing should come near our place. When visitors come and they understand they are with me and "okay", they are fine with other people—some are friendly, and some are reserved and keep their watchful distance.
I feed a good quality dry food but, unless you have a place they can get into to eat that the sheep cannot (sheep love the grains in dry dog food), be prepared to feed them only what they will clean up right away (and I usually mix a bit of canned food in to encourage this—especially in the heat of the summer when their appetite is not as good. In the winter I try to provide an extra course of fat for them (beef marrow bones, olive oil on their dry food, meat scraps, fats, juices mixed into their dry food). I have not seen dysplasia but don't know that it might not exist in some. And like any large breed, 10-12 years old is getting up there in age. Lady died of congestive heart failure at 11 and Tramp (her work partner), who is almost that now, is getting quite arthritic.
I don't believe that the dogs have a stubborn streak, as much as the fact that they are a very intelligent dog and will work and gladly die for you and their sheep as trusted partners. You don't order them around or "train" them as you're used to with other dogs. My first Pyr came from the heart of downtown, metro Syracuse, NY, and had never seen a sheep at age 4. I penned her (livestock panels or electronet) where she could be with the sheep and get acquainted when I was not with her. Then I'd walk her on a leash around the perimeter of the field so she could learn her boundaries, and through the flock so she learned to move slowly and not race through or at them. Then I gradually dropped the leash and let her move on her own with the leash or long-line dragging so I could easily catch her up if need be. Then with no leash, but I'd work nearby and keep an eye on things and then trusted her on her own. She never disappointed me. I've used basically the same method with other Pyrs and so far, it's always worked. Another reason they need to be penned at first is to get them to a point where they trust you. I recently took in a rescue/stray from the SPCA who obviously had been terribly mistreated, and it took awhile for him to trust me—now he's the dearest, most loving dog but very afraid yet of other people (he may never be good against two-legged predators). We're working on getting him to realize that, while it's fun to run after the sheep if they break and run from him, it's not really the right thing to do!
I really love having two dogs who can work as a team, one "on duty" while the other rests, and one there to back up the other if needed with numerous predators, etc. And I just love watching how they do work together.
— by Mary K. Gloster