They do if you only let the pup on unlimited registration go on a co-ownership.
One breeder who's dogs I am seriously looking into does this. It's pretty awesome, because she puts in the contract that as co-owner she has to approve any breedings, has a list of required health tests that must be passed for both sire and dam before a breeding, and the mate being picked for the breeding must be approved by her. If the contract is violated, she has the right to regain full ownership. So, if someone did take one of her dogs and try to breed it willy nilly she could technically go and pick it up as it would become hers. Also, I think as the co-owner she has to sign off on papers for any litters.
I don't know if someone can dual register a co-owned dog with another registry as being owned by one person, without the co-owners signature either.
It seems like a pretty good system to me also, because nobody knows a breeder's lines better than they do, and so if you are planning to breed one of their dogs then they are the best person to go to for opinions when looking for a suitable match.
One breeder who's dogs I am seriously looking into does this. It's pretty awesome, because she puts in the contract that as co-owner she has to approve any breedings, has a list of required health tests that must be passed for both sire and dam before a breeding, and the mate being picked for the breeding must be approved by her. If the contract is violated, she has the right to regain full ownership. So, if someone did take one of her dogs and try to breed it willy nilly she could technically go and pick it up as it would become hers. Also, I think as the co-owner she has to sign off on papers for any litters.
I don't know if someone can dual register a co-owned dog with another registry as being owned by one person, without the co-owners signature either.
It seems like a pretty good system to me also, because nobody knows a breeder's lines better than they do, and so if you are planning to breed one of their dogs then they are the best person to go to for opinions when looking for a suitable match.