The tenants esstopal letter should have included that information. It is too late now for the tenant to come forward and make their clai now unless they have documentation themselves to prove they paid.. Chances are you will not see their LMR anyway. You are likely SOL.
If they do pay their last month tell them to go after the previous landlord for the money since he still has it.
The closing agent has no responsibility in this.....they simply close the transaction as per the contract language and written agreements provided by the parties, they don’t go investigating/verifying such things.