Speaking as a former claims adjuster (now over a decade) there’s screwed and then there’s screwed.
First let’s talk about the carrier. They’re the least at risk in some ways, because they have clear contractual limits (leaving out No Fault states, and even then…). They’re going to pay out to the limit, and then they’re in the clear, absent some uncommon circumstances that I’m about to mention.
First - they open the floodgates by authorizing payments / settlements before assessing the loss. I’ve mentioned in previous threats about how dangerous state minimum coverage can be in several states, especially California, where the property damage coverage can be as low as five grand (!!!).
But if I as the adjuster on behalf of the carrier authorize payments, with such low limits, especially in multi-car or multiple owner (ask me about the 5 car, 4 building accident, no, wait, DON’T) losses, then I and the carrier are screwed. Because I have the obligation to pay out in a fair and complete manner to the limits of the coverage, but that means I need the total amount of damages so I can pay proportionally to all claimants. If I pay out three thousand to the poor old lady who lost her only way of transportation, but there’s still 7 people in line that the remaining 2 grand isn’t going to cover… again, screwed.
So in such circumstances, I would have had to say “I can’t pay anything out until ALL claims are submitted” which could take months to years. And that was not a fun conversation.
Secondly, and much more rarely, there’s the circumstance where there is possible negligence on the part of the insurer. I was a licensed P&C agent before I was an adjuster, and part of my job was to be on the record (recorded) in suggesting appropriate coverage to someone and NOT just quoting them state minimums no matter WHAT they asked. Because if I sell a homeowner state minimums without at least offering reasonable coverage, I have not done due diligence, and a smart lawyer would come after us for that.
In terms though of your personal exposure AFTER your carrier had paid out, as suggested upthread, that’s the realm of lawyers. A smart claimant ('s lawyer) will go after the reasonable limits of all possible existing coverage, and some of the negligent issues above, but they’re likely to avoid the whole “blood from a stone” route. But liquid assets, real property (depending on state laws), etc., well, that’s why I mentioned the duty to insure properly for your assets.