Got into an at fault accident with no liability insurance, what is going to happen? - North Carolina?

Without liability coverage you will have to pay for the damages out of you own pocket. If you don't someone, either the other party or their insurance carrier, will sue you and get a judgment against you. That judgment will be good for 10 years, and can be renewed for another 10 years. You may have no money now, but surely you will acquire assets they can attach over the course of the next 20 years.