As noted, transfers are between memberships, and not contracts. I think there are times when we use words interchangeably here on the DIS.
So, for others:
A membership is what holds your contracts. When you buy contracts that have the same UY and the same owner, they go in one membership. Anytime you buy more contracts with the same UY and same owners, it is an add on to your membership.
People will say I am "adding on to my contract" but in reality, it is to the membership. Contracts are deeded real estate interests and can not be changed. As you add on, your contracts get numbered with XXX.1, XXX.2, etc.
If you buy a different UY, or own a contract with different owners, it is a new membership.
Transfer is when one owner moves points from their membership to another membership. It is limited to one in or out per UY, unless you are the owner of both memberships and then MS has been allowing more than one (though that could stop at any time).
So, points associated with your contract can not be saved when you sell the contract unless you had another membership to transfer them to for use.