Our local humane society is the strictest--it seems to be rare for them to adopt out a dog because they have such strict rules--when you visit their website the same dogs are there forever. They will only adopt dogs, even the biggest of dogs, to indoor homes....and those homes must have a fenced yard. Their adoption form says they can do a home check, either prior to adoption or after, even months/years after? I don't know if they ever actually do post-adoption home checks, but their form indicates that they can.
the local rescue also specifies indoor homes, but they are lenient on fenced yards--they prefer to have dogs hand walked as opposed to having them put out & left in a little fenced yard. You must provide a vet reference, and if you don't have a vet reference then they will do a home check. Their animals are all in foster homes, they do not have a facility of their own. The problem with them is--from what I've heard and seen from people that have looked at getting dogs from them--their foster care people are often not very good at evaluating their animals. As one example, a friend of mine went to meet 2 of their rescue dogs a couple weeks ago--she wants a dog that is similar to what we expect of a dog--obedient, hangs around while her people are out in the barn/doing chores, good with cats--was assured that these pups were fine with cats, good at sticking with their people...got there to see the pups (4 mos old) and they are kept in an apartment, separated from the cats by a gate, foster mom said that she knows nothing about dogs & has never had dogs before these 2 pups so doesn't know how to train them, when questioned about cats admitted that they are rarely around cats and "usually if they jump on the cats & they cry the puppies will back off & leave them alone but this morning they just keep jumping on the cats", the pups had basically no manners whatsoever...my friend decided that she didn't want a pup that has had that sort of a start in its "training" and so didn't even request adoption papers. She wants a dog that has had better training up to this point or else she'll get a younger puppy that she can train right from the start--she was very disappointed that these two puppies were so different from how the rescue advertised them.