I have heard of issues like this happening on expired listings - since all of the data the agent needs to put the home back in the MLS is in the history for that address. But, there should still be a signed listing agreement on file. There is no excuse for an incomplete file. This isn't rocket science. There is a process that should be followed every time an agent takes a listing.
So, this is a trick question: if no agreement is signed, can it even be put into MLS? No.
Can a broker earn a commission without an executed written agreement? Tough question. It goes to ethics. If a car mechanic fixes the problem on your car, do you owe him anything? There is a principle of unjust enrichment where someone does something in reliance on an expected situation or outcome, but the situation turns out to be false or reversed. The recipient of rewards due to the efforts expended by the someone cannot be granted to the recipient without compensation to the someone, but whether this applies is a good question. You'll probably have to ask an attorney if you can't sort it out on your own or with the "agent".