ColdBrook: "I immediately guessed you were in the northeast when I read your post about all the shelters have are pit bulls...that is exactly what I found when I tried to find a dog through local shelters about 10 years ago. There was NOT even one dog at the shelter(s) that wasn't at least part pitbull...I was shocked."
It isn't just the Northeast -- it's many places. The Pit fighting breeders are all over, and they breed their dogs like rabbits, but only keep the most aggressive pups; and then they unload the rest by turning them loose, giving them away, or turning them into the local shelter as 'found' dogs.
Local shelters seem to have a new game they're playing, at least here in the PNW: They take in all the normal dogs that are turned into them, euthanize the unadoptable ones, and then they turn most of what is left over to the BIGGEST rehoming operation in the region. Here, this is Seattle Humane. This transfers the expenses to someone else.
The ones they keep are the pit breeds that don't
seem aggressive, a few short-haired cats, and the animals that the big operation doesn't really handle: rabbits, chinchillas, rats, ducks, chickens, etc. This keeps their expenses down, even though they still get the same percentage of taxes through the county.
The chances aren't great for getting a decent, well-mannered, healthy purebred rescue for a low price. If you have a purebred rescue (multiple breed) in your general area, they usually don't have a facility, all their pets are living with volunteer fosters. They've learned from experience that cheap dogs tend to be throw-away dogs. If you want a purebred, you'll have to pay. Your best bet online may be PetFinders at
https://www.petfinder.com/ They have a decent enough reputation, but be sure to CYA.
If you find a dog on Craigslist (etc), be sure to have it scanned for a microchip, as many of them are stolen. And be sure to follow all of the above tips for scams that can possibly be applied to pets. If they can be, they will be.
BTW, Yorkies have been bred so small that they now often have built-in health problems, like lymphangiectasia, portosystemic shunts, and keratoconjunctivitis sicca. Buying a dog from a REPUTABLE breeder can be cheaper than buying one at a lower price and having to deal with health problems.