This situation had to do with a cat.
A friend of mine posted on FB that a thin black cat in his area had wandered into his house around midnight one night and decided to stay.
He found a tattoo in the cat's ear and took it to the HS to trace the tatt. They found the original owner right away - her cat had disappeared FIVE YEARS before and she thought he had died.
She is now living in a no-cat place, so Midnight - the cat once known as Titan - went to live with my friend!
I know it's less likely that dogs run away without being noticed, but just saying it's worth checking out the background. In the cat's case, the owner would have had first dibs - but she couldn't have a cat where she was, and perhaps also decided that since my friend had taken such trouble to find out about the cat, that he would have a good home.
"You can say any foolish thing to a dog, and the dog will give you a look that says, 'Wow, you're right! I never would've thought of that!'" -- Dave Barry