Three million is high. I remember back in the 1980’s a local Canadian newspaper ran a cautionary tale about auto insurance in the USA. Some fellow from Canada was sunning himself on a beach in Florida when an idiot in a vehicle drove over him. (You can drive on some Florida beaches) Turns out the driver was from some hillbilly state like Kentucky or somewhere, and the requirement there at that time was for minimum $25,000 insurance.
I have heard something about, for example cancer treatments in the USA, that the medical insurance company cannot cut you off in the middle of treatment; but if you are say, a child with leukemia, you had better never see a doctor once you hit your lifetime limit on that insurance. They will pay whatever it took to finish the treatment, then you are cut off and good luck finding any other insurer.
Not sure if this same logic applies to therapy after a car accident, or if the insuance company cuts you off when the bills hit $3M. I guess the other interesting question is how you prioritize the bills. If I cause a spectacular 20-car and tractor-trailer pile-up, do medical bills get first dibs, or does everyone submit their bills and settle for X cents on the dollar? What about projected future care costs?
As for the direct answers, yes, if the insurance limit is reached, bankruptcy is your best option. Then, for the victims, the US Medicare system for the poor, or the victims’ own medical insurance perhaps, would kick in. If that does not cover physiotherapy or rehabilitation, well, sucks to not have universal health care.
OTOH, as mentioned above, $3M is still a LOT of money for 99.999% of accidents.
The other point would be that in lawyer-happy USA, the people needing money would drag anyone and everyone into the lawsuit. Even the tiniest piece of contributory liability would mean that those additional defendants would have to make up the difference under joint and several liability. So include the county or state for the unsafe road signage or poor road maintenance, sue the vehicle manufacturer for poor brake performance, the rental company for failing to ensure you knew how the safety features worked, the GPS maker for telling you you could do 60mph when the road conditions would suggest less… The lawyers would get very rich no matter who pays.