What if the copy isn't a hard copy but rather a PDF? The PDF never changes hands. There is a PDF on Bob's computer and then a PDF is created on Carol's. Even if we can agree that Alice owns Bob's PDF, why should she own Carol's?
I think this particular argument boils down to "what if Carol was the one who made the copy by observing the bytes on Bob's computer?"
I don't see a way to close that particular loophole by contract.
Surely, the original contract would contain a clause to discourage this eventuality, e.g. "If Bob allows a copy to be made, he hereby requests to be hung, quartered and drawn." (Which incidentally is probably where today's punishments for copyright infringement seem to be heading.)
But this would only be unfortunate for Bob and it would still leave Carol in the clear, as you say.
I think there is a case to be made that while you can't completely derive copyright from property rights through this form of contract, you can at least have something quite similar. You can allow people to view your material while essentially holding them at legal gunpoint should they fail to protect it. Once the information is out you have no rightful claim on it, but that requires that the last party in the chain of contracts is ready to suffer the consequences.