I think the answer to the first question is yes, I can't say about the second question. A seller brings in a horn to sell on consignment and negotiates the terms with the dealer. The dealer finds a buyer, completes the sale, and pays off the seller as agreed. But there's a catch. Sticking in the case was a nice vintage mouthpiece, and that finds its way onto the dealer's shelf. His "consignment percentage" on the mouthpiece is 100%, since as far as the seller knows the mouthpiece sold along with the horn.
If you are selling a horn on consignment, make separate arrangements for any mouthpiece that may accompany the horn - keep it, sell it on your own, or negotiate a separate consignment deal.