Yes, assuming the grandchild was at fault (since liability is based on driver fault), then the grandchild (the driver) and the grandparent (the car's owner, who permitted the grandchild to drive) may both be liable beyond insurance limits. Your insurance limits do not limit your liability; it limits how much reimbursement, indeminification, etc. you get from your insurer.Example: say that the grandparent had $25k of liability insurance on the car and the grandchild was at fault in a car accident. Say the injured driver gets a judgment for $100k. Insurance will pay $25k; the grandparent and grandchild are together liable for the other $75k; one or both have to pay that amount. The plaintiff or person suing (the injured driver) can choose to go after one or the other; if the grandchild appears insolvent, but the grandparent has assets or an income, the plaintiff could legally choose to go after the grandparent for all the $75k. The grandparent in turn could cross-claim against the grandchild to make  the grandchild contribute to that (assuming the grandchild has money to contribute).