What happens in a car accident if both cars involved do not have insurance and the car at fault was drunk driving?

If neither vehicle was insured you will have to sue the other party in order to collect any damages. Drunk driving is a contributing factor but really whichever party is at fault for any reason will be liable to the other party. The bad news is that if the person did not have insurance the probably don't have assets to pay the damages. This is why you need insurance and uninsured motorists coverage.