So if I understand this correctly, your birds were confined and protected inside a run, but you believe a dog somehow opened(?) the coop door, then went into the coop, through the pop door into the run and killed your birds there? Key questions would be how it managed to gain entry through the coop door? Not saying this is your fault.....not in any way......but more of a learning opportunity as to how this could have happened so you and others like you can avoid whatever it was that resulted in the outcome you had.
Other than that, if you go to the sticky at the top of the predator post, there is a "worst predator" thread with a poll attached to it. Out of the 18 named predators in the poll, raccoons and dogs manage to account for over 40% of the votes. So they are a serious threat, and dogs in particular a troublesome one as it not only involves the predator.....the dog......but by association, the owner as well. Often times the owners are as much of a problem or more than the dog itself, as they will defend it as if it were your fault their dog killed your birds. Some are responsible and will own it, others will not. You never know how they will respond until they are given a chance to.
But putting that aside, with the birds, it is safe to assume the worst is coming....so you plan accordingly. In my experience, the absolute best method of dealing with your neighbor's dog is to greet them with a blistering hot electric fence. One dose per dog is usually all it takes for them to leave....and never to return.
https://www.backyardchickens.com/threads/dogs-and-electric-fences.1210854/
Due to an influx of strange new dogs the past month or so, I recently pinned some bacon strips to the hot wires to help these new dogs along on their journey of discovery. It seems to have worked wonders. Birds are still alive and the visiting dogs have never been back.
I think it is safe to assume that if you have chickens, you will also get visits from dogs. They can't help it. Hard wired into them. And given a chance, they will do a lot of damage. So you don't give them a chance. You bust em on their very first visit and do so harshly.