Even if your dog gets stolen after being chipped, it still increases the chance of getting them back. Because it can provide proof of ownership as well as identity (say if you offer a reward and someone brings in a yorkie similar to yours but it's not). Also depending on the brand and offers of the microchip, it can offer a sort of shout out to nearby vets, shelters and people part of the program (at least that's what the program I use for my chip). Granted if the thief never takes them to a vet and you don't know or have an idea who the thief is, yes, it's almost impossible. But chances are, if they are thieving for money and the yorkie is fixed (thus unable to be bred for more yorkies), they'd sell it to someone who's most likely to take them to a vet. Of course, if the thief was wanting the dog themselves, then yea that wouldn't work much. Either way, it's offering more chances than without (even if slim). The chip I gotten can even be scanned if my girl is somehow overseas, as long as they use the standard scanners. I went through AKC to get my chip etc and just have my vet insert it for me. Costed me a lot less with more benefits offered and the vet did it for free
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R.I.P. Mick & Mandy (before 2010), Mila - 4/3/15, Chloe - 2/18/16, Kimchi - 6/2/2021