All pets from a shelter or rescue will be fully vaccinated and health checked prior to adoption. Under the conditions of most adoption agreements the owner must provide proof of regular vet checks and vaccinations in future years.
A purebred rescue does provide the possibility of obtaining a purebred dog or puppy, even though they cannot be used for breeding purposes. This allows the new owner to select exactly the breed he or she wants, without having to wait for that breed to come through the regular shelter.