Most "rare" breeds have rescue organizations funded and run by the breed's national breed club. For example, Ibizan Hounds in need of rescue usually end up being fostered and placed with the help of the breed's national club, IHCUS. People who are active in the breed are best-suited to place rescue Ibizans in appropriate homes, since they are experienced with the breed.
Is there a particular reason you want to open a rare breed rescue, and do you have any experience in a particular rare breed?