Where can I find a dog under 40$?

Animal shelter.

I don't reckon you'll find a dog that cheap at a shelter even, unless it was on it's last legs. 'Backyard breeders' are your best bet to find a dog under $40 but really it's just irresponsible, a lot of backyard breeders are not to be trusted to treat their dogs well and should not be encouraged to breed their dogs. But if you're looking for a cheap dog what you're going to find is a 'cheap' dog.
Hell, I got my dog FREE from a backyard breeder (a friend of mine, not cruel just a little lazy with desexing their 3 dogs) and he has already cost me thousands in vet bills because of bad genetics. Not to say spending hundreds to thousands on a dog from a trusted breeder would make you safe from expensive vet bills, but it's just a better start to know what you could be getting in to.