Thanks for the update and comments. Considering your circumstances, I think you are wise to leave your birds confined to the safety of the run and house. My daughter lost her first flock to a fox and since then has kept her birds confined into the house and run and have mostly been safe. But...
BTW, on the neighbors dog, rather than the dog got shocked and ran home scenario, consider a possible alternative......they one I see playing out here on BYC time and again. No fence, dog kills a bunch of birds. I get mad, neighbor may or may not be apologetic, but if they do nothing except...
Not sure if you read the entire thread that was provided, but if not, I encourage you to do so. Crib notes version is birds running around totally unprotected are not unlike what the insurance industry refers to as an "attractive nuisance". They are a prey animal and draw the notice of all...
I see threads like this and marvel at the drama........since none of it has to be that way. Once shocked, you can hardly force a dog to go near a fence.......
https://www.backyardchickens.com/threads/dogs-and-electric-fences.1210854/