There are actually three parties here, the legal representative, the impostor and the counterpart. Only the impostor is definitely illegal, and both the legal representative and the relative person may be the injured party. But someone must bear the loss in advance.
If the impostor can afford it, of course not. But if you can't afford it, the counterpart and the legal representative will actually suffer. The law stipulates how to distribute the losses between the two parties.
There are legal provisions on agency by estoppel, malicious collusion, bona fide third party, duty behavior and so on.
Whether the legal representative and the company should bear external responsibilities and then recover rights from the impostor depends on the specific case and evidence.