What happens if the driver who is not at fault for an accident does not have insurance?

He will be left with a wrecked car! He will also have to pay for damages to any other vehicle(s) involved in the accident. However it can vary from country to country, but in the UK, not having Car Insurace is illegal, so the uninsured driver would be a bit screwed!
I think in the UK you can even end up serving a short-term jail sentence for repeatedly dodging insuring your car. I'm not 100% though.
Even if the the insured driver is at fault - the uninsured driver will be left paying for the mess himself - and will have to fix the car with his own money.
But if you live in the US - then this could be completely different.