Many rescue groups exist for purebred cats. Some operate on a national basis, such as the Cat Fanciers' Association Breed Rescue, and others operate in only certain areas, such as Purebred Plus Cat Rescue, which operates only in the Western United States.
Some purebred cat rescue groups accept cats of any pure variety, but most focus on rescuing a particular breed of cat. For example, the Japanese Bobtail Rescue League operates nationwide to rescue only purebred Japanese Bobtails. Teacup kittens are just small cats and are therefore not necessarily purebred cats. If a particular teacup kitten was bred from purebred parents, the kitten would be eligible to be rescued by the appropriate purebred cat rescue.