Cryptic already has said, they have a solution for that special special project. No one will be stuck on it once the resources are no longer available.
My best guess is that the rest percentage will be converted into a dilithium amount that is comparable to the other special projects.
So if your Breen Ship Ornament is 50% done, you need to use 100k dilithium to finish it.
Don't take my word for it, just seems the most "Cryptic" way to do it IMO.