State laws differ but in general yes, if you were at fault in an accident and caused damages to another party which their insurance company paid, that insurer can now come after you for the monies they paid out since your insurance policy was not in effect (lapsed) at the time of the accident and you were at fault.

It is normal practice for an insurance carrier to subrogate with the at fault party if they have paid out money on their policyholder's behalf. In most states you will be required to make restitution with the damaged party or their insurance company in order to not have your license and/or vehicle registration suspended since you were driving illegally without insurance.

If you were at fault in an accident while driving without insurance you could find out from your state's insurance regulatory body or DMV what steps to take to make the other party whole so you are not penalized further than the consequences you will face for being an uninsured motorist. In many states if you cannot pay in full all at once for the damages you caused you will be able to set up a payment plan.

Driving without insurance has many consequences one serious one being that your assets could be at risk if you cause an accident and the other party was seriously injured or their car's ACV or repair bills are quite high and you cannot afford to pay the party or their insurer back. Follow this link for instant car insurance quotes so you will not be an uninsured driver any longer.