Nothing happens. And by nothing, I mean settlement wise.
It's only a limited power of attorney (very limited), and you kind of signed one with them already, so it's not a big deal. When you signed your application for insurance, you agreed that the insurance company would do all the legal negotiating on your behalf in the event of a claim. It says that right in the contract, and you can look it up if you feel like wading through all that legal mumbo-jumbo. The contract you already signed (or legally accepted) is binding in any court of law, so the document they're asking you to sign now is just a formality.