To be clear, if you have Property Damage Liability coverage with a $10,000 limit that is used to pay for other property, not your car (if you are at fault). If your car was damaged and the accident was your fault, then your physical damage coverage would pay up to the actual cash value (minus the deductible).

State laws differ however once your insurance liability limits are reached if the other person does not agree to take only that payment as a settlement to the accident damages then normally they can come after you personally for the difference of what the damages cost to repair or remaining ACV of their vehicle if it was totaled.

It is important to have high enough liability limits so that if you are in an accident the limits will cover the damages you caused to others, both bodily injury and property damage.

Likely what will happen is that the person will take the money offered by your insurance company, which is sounds as if it will be the full limits of your policy of $10,000, and then seek any other monies they are out by contacting you directly for payment or taking you to court to seek a judgment against you for the extra money they are out.

So your personal assets are at risk if you are unable to make payment to the other party or if they go through their own insurer's collision coverage for full payment and then that insurance carrier comes after you for repayment (subrogation).

This is why we advise for a policyholder to buy the highest limits they can afford. If you select limits that are too low, you could be putting yourself at risk financially. Like in your situation where it appears that you caused a serious accident where damages exceed your limits so 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.

In the future by purchasing an auto insurance policy with liability limits to account for both your current assets and future net worth, you can help protect yourself against this risk. As for dealing with your current situation, your insurance provider's claim department can tell you more on what they believe will happen with the claim settlement and if you should get yourself legal representation.