If there was an agreement between Realtor A and Client, then that agreement should remain in effect as written unless there was a provision in the agreement that allowed the client to negate the agreement. The agreement could also be terminated or modified by consent of all the parties to the agreement.
However, if there wasn't a termination provision in the agreement and the agreement wasn't terminated by mutual consent of all the parties to the agreement, then the agreement between Realtor A and the client remains in force.
The question then arises as to whether the client had the ability to sign an exclusive agreement with Realtor B. Or, more accurately, whether such an agreement could be enforced. My guess is that a lawyer would say no.
As a practical matter, one resolution to the issue would be for Realtor A and Realtor B to share the commission. From a legal standpoint, though, one or the other (my guess is Realtor A) would be entitled to the entire commission.
Again, though, you need a lawyer to review the documents and provide an opinion.
Read the agreement signed with Realtor A. Often those agreements contain a phrase that talks about a protection period (3-6 months) if the house sells due to the efforts of RealtorA, with someone who saw it while they were showing.
BUT (and this is an important "but")... if they sign up with a new agency... the new agency's contract (REALTOR B) supercedes the first contract.
The fly in the ointment here, is: did the seller have the "right" to exit the contract with RealtorA? Was there ever a mutual release?
without more information, the water here is very very muddy.
I am NOT an Attorney but I might think the original contract as well as the later is unenforcable as both owning parties didn't fully execute the listing agreement. Just my two cents. I would be curious to know the final answer. Good luck.