All this varies by state and by insurance carrier. I’m in FL.
It would behoove you to contact your insurance company. That’s what you’re paying them for. If that driver suddenly develops “whiplash”, your insurer will protect you. But only if they know about this accident before the suit is filed. Your policy almost certainly contains a clause requiring you to report everything and absolving them of responsibility if you “forget” to do that.
By coincidence my own car was hit similarly but worse in early Sep. The other driver and I were cordial, exchanged info, talked to the cops, etc. Mine was (barely) drivable to my nearby shop while dragging parts on the street. His was tow-away only. No injuriess.
I promptly reported the accident to my company (USAA). He reported to his (State Farm). I did all my interaction with USAA. Other than giving State Farm a statement when their claims worker called.
State Farm promptly admitted liability.
USAA evaluated my car and decided to total it using their evaluators, their criteria, and their own ideas about payoff amounts. My policy has a feature that pays 20% over the total-out value to help you pay for a replacement car. That add-on extra had a small incremental premium; it proved to be a very good investment.
Even without that top-up USAA said the other carrier was going to offer far less as their total-out value. They’re just hoping you’ll go away just barely satisfied enough to take the deal while grumbling. Very different motivations.
About 10 days after the accident I got my check (ACH transfer actually) from USAA. Ref @gnoitall, I still owed money on the car. The insurer paid off the lender directly & sent me the overage between amount owed and the total + top-up settlement.
In my case I wanted the money, not a damaged car. I was in the wrecked car biz many years ago. Unless you intend to keep that car until it’s a musty rusty ratty bucket of bolts that barely runs and scares the neighbors, keeping your total-out is a money-losing disaster from end to end. Formerly professionally speaking, don’t do it. No reputable dealership or big used car outfit (e.g CarMax, AutoNation, etc.) will take it in trade, and private parties will run, not walk, the other way once they see the CarFAX. Which they will.
USAA has since informed me they’re going after State Farm of all of it. My deductible, the base total-out amount, and the top-up payment. Not my problem since I’ve got all my money already, but I wish them well.
Bottom line: if you don’t want to get screwed, deal with the people who know you’re their customer, not somebody else’s customer.
And take the money, not a bent vehicle with a scarlet A spray-painted across it’s windshield for life.