I have rehomed a dog. I had a cocker spaniel that loved to run! She needed constant supervision when she was in my (large) backyard, otherwise, she would get a good gallop going and go OVER a 6 foot fence. I got more phone calls than I could count from my daughter's school (2 blocks away) telling me that Belle was up there visiting again. When I got put on bedrest with my 2nd daughter, I tried to get her to go pee out in the garage on a pee pad. She ate through the alternator wires in my mini van.
I ended up sending her to my parent's house with the understanding that she would come back as soon as I had my daughter and could stand there with her outside again. Problem was, my parents fell in love with her and didn't want to give her back. She lived another 13 years with them quite happily as only (spoiled) doggie.