State laws differ however in general if you drive someone else's car and cause bodily injury or property damages above the limits of the policy then usually both you, the driver, and the car owner can be held liable for the excess.

If you were at fault in the accident you should know that normally the car owner's insurance would be primary and if their liability limits are exceeded then your auto insurance as the driver would be secondary and may be used. If your insurance policy cannot cover the excess needed then in many states you and the car owner can be sued by the other party who has been injured. This is why it is important to have high enough limits on your liability coverages. In the event of a serious accident, you want enough insurance to cover a judgment against you in a lawsuit, without jeopardizing your personal assets.

If you select limits that are too low, you could be putting yourself at risk financially.
For example, if either you or a driver covered by your policy cause a serious injury where damages exceed your limits, you will be held responsible for the amount above your limits. To make that payment, you could be forced to liquidate property, savings, and other assets, or your future earnings could be attached. By purchasing liability limits to account for both your current assets and future net worth, you can help protect yourself against this risk. This means both you as a car owner or a driver.

To find out what your state laws are regarding this situation where the car owner loaned out a car and the driver was at-fault in an accident and caused bodily injuries whose costs exceed the limits of the owner’s policy you may want to speak to a lawyer. You may also try your state's insurance regulator who can give you consumer advice on the situation.