What many people don't realize is that there are specific breed rescue organizations for almost every breed of dog, placing dogs in need to new homes. (rivertrailahandpetlodge.com)
In addition, there are cat breed rescue organizations that take in cats of specific breeds that have been abandoned or otherwise can no longer be cared for by previous owners. (cat-lovers-only.com)
If you are dead set on a cat of a specific breed, there are also breed rescue organizations to explore. (thesprucepets.com)