[Peretool]

As others have said, you have to weigh your quality of life, the other dogs quality of life and Gauges quality of life. You also have to factor in safety, expense and the details I can't imagine of caring for a mentally ill dog.

I don't see staying where you are as a real option considering the condition of the house and the freaky underwear stealing neighbor. Living under that kind of stress for an extended period of time isn't healthy for you mentally and that passes off to the dogs. Plus, since the place was broken into and a dog was let out it is entirely possible staying there is risking the lives of your dogs because any one or all of them could be stolen or simply turned loose in a future break in.

The way I see it, you can rehome him, put him down or accept the burden of his care for the rest of his life and rehome a different dog who has a chance of getting a permanent home and living a good life. Considering everything you have said and how difficult I imagine the situation to be, I would probably euthanize him. Course, I am not in that situation so I can only speculate as to what I would do. Much easier than actually having to make a decision and do it.