With rare exceptions, car insurance follows the car and if you provided consent to use the car, your insurer would provide primary coverage to the user. Similarly, if he/she had a personal car insurance policy, it would likely "stack" as excess protection.
The more important issue is not whether you can be sued, but rather whether you could be held liable for damages caused by negligence of the permissive driver. Yes you can be sued! Generally speaking the only requiriement to file a lawsuit is not legal standing, but rather the ability to find the courthouse and pay the filing fee.
As to liability, that is an entirely different matter.
If the driver was on a mission or errand for you when the accident occured then his/her negligence could be imputed to you. Additionally, if you had knowledge that the driver was unlicensed, intoxicated, wreckless or otherwise impaired then you might be held liable for negligent entrustment.