Foster homes are responsible for caring for a rescue pet before it is placed for adoption. Some breeds have little need for foster homes, as they have a long waiting list of prospective adoptive homes, and few being placed for adoption. Other more popular breeds have more calls for pets than they can possibly rescue, and extensive network of foster homes, and an adopting family may even have their choice of animals. Well, first off, for dogs you'd usually get an adult whose chewing phase, housebreaking phase and general puppy wildness are gone. Your dog may come pre-trained, and might even know a few tricks.
Adult cats are more laid-back and are often more affectionate.
Many are already declawed, and most males are neutered as people are more likely to neuter their male cats than their male dogs. You would know exactly how big the dog or cat would get, and would have a good idea of the individual personality. Last, but not least, you would be giving a deserving dog or cat a good home. Very rarely, Breed Rescue gets a kitten or puppy, sometimes from a family that made a wrong purchase, sometimes when a pregnant female with a litter is surrendered. So, you'd still have lots of growth time left in your rescue.