Oops! Now hold on a minute! There were some differences with my wife's dog. For example, we held the dog ransom and demanded large sums of unmarked bills from the next store neighbors. When they failed to pay, we kept the dog and her puppies to make a new coat for my wife!!!!! When their meddling kids came up the driveway to take him, we hit em' with the power washer!!!! 
Yeah, there were some differences between our story and the cats. For example, this dog was wandering the neighborhood for several months and living at various houses the whole time. After "found dog" signs, calls to the dog pound, lost and found type adds, and talking to various neighbors, the dog ended up staying between two houses, and eventually ours. The neighbors were supportive, and everyone assumed when the dog would go missing, she had merely gone home (in reality she was vacationing at various other neighbor's houses- never an owner). People were concerned as the dog was wandering onto some busy rural highways and was going to get hit in a matter of time. After about 6 months, I guess we fed her the best, or had the best furniture. She got tired of walking around and plopped on our couch for good!
That is what got my wife calling about ownership laws. In Va. (I think) it is only 7 days of possession and if the "adopter" spends money on the dog and can provide receipts (vaccinations, etc- which my wife did /checking for implant ID, etc..), the original owner would be required to pay the new owner or relinquish control of the pet. I remember thinking how lax that seemed, and concerned that could lead to a lot of "situations", but evidently it doesn't.
Edit- since typing my original comment, dog has not moved off couch and is still snoring away. If you want a free "grey market/fully laundered" dog, please pm me.
Upon re-reading Noah's story I saw the thing about the cat originally (until recently) having a collar, which blows some holes in my theory. Weird!