So different in the States than here when it come to such things
First off we dont have law firms, at least none that specialize in accidents ( ambulance chasers ) , and in regard to injury well that of course need to get fixed and so it will via our public healthcare system.
If you have gotten any loss of ability to work that will also be assessed by the public, but here is when it turn ugly, that public system are a mess, and thats putting it nice.
But in the end those guys will reach a verdict,,,,, one you can fight if you dont agree, and only then i think will a sort of court or arbitration be needed.
If you are entitled to some kind of payment for pain / grief / loss of income, thats handled by the involved insurance companies i believe, again you can complain if you dont agree on the result.
Either way if you do not agree, then you can complain and some one will for free handle your case, naturally this mean that financial compensations for something are far from the same over here than in the states.
So you should not have to reach for your wallet as such here, but still if you get into such a spot your economy will get under some form of pressure as these systems seen to work slowly and be quite rigid.
If you go to the hospital for some weeks, and after that cant work for a while, thats of course where you will loose out on income, but its not like 100%, at once you will get sick pay which are close to your regular pay, and that you can get for many months, before you might eventually be kicked down to welfare thats not a well paying gig but still enough for you not to starve to death.
So in that regard yes you will loose some money, but hospital / treatment ASO you do not have to pay for right then and there or by having a insurance for that.
Danes are encouraged to have a accident and injury insurance, if you have car insurance that will also hold a injury part that will cover anyone you might injure, only if you have the accident insurance will you also be covered VIA insurance in some way ( this is then on top of anything public compensation )
The accident insurance ( not only traffic accidents ) also cover other things of your own and belonging to others you might ruin, if you dont have such a insurance you can get in a spot where you will have to pay up yourself, and if you cant right then and there the public will pay for you and then take the money over your taxes or pensions / welfare payments,,,, either way the public always get their money, i always said owing money to a biker gang are more easy, at least they will supply you with a sawed off shotgun and drive you to the nearest bank.
The accident insurance also cover you if you have been to the movies and gotten a little fired up and so when you get out you feel like demoing to your friend your kungfu skills from when you was a kid and had the green belt, Either way when you then kick in his teeth, your accident insurance will cover that, cuz of course you dident mean to kick his face in and so it was a accident.
And dental work are not covered by our public healthcare system ( dont ask me why its really weird to me, and probably why Danish dentist are some of the most expensive in the world )
A few years ago a American was killed by a little Electrical car the municipality in Copenhagen use for sweeping the streets ASO, the thing was not maintained properly and engaged itself and ran over the American killing him.
His family did not receive anything other things than a " we are sorry"
where as if that had happened in NYC or any other American town, the town would have been taken to the cleaners.
Either way, one will be smart to trust no one, and thankfully technology can do a lot for us in this regard now