I was involved in a car accident but the person at fault has very low property damage coverage, can I settle with his insurance for that amount?

Do you have underinsured motorists coverage?

Yes.

Do you have UM insurance on your vehicle, for both property damage and personal injury? If the adverse driver's insurance is not enough you can make a claim against your own UM policy. The driver of the other vehicle is responsible for all damage caused, but you cannot settle with his insurance carrier and then go after him IF you sign a release of claims form with the insurance carrier. It is their job to make sure if they pay you, that is all you get from not only them, but their insured. If you want full value of the property damage from him, you will have to take him to court which will also get his insurance money and a judgment against him for whatever is left if you prove it. However, the question would be, does he have the money to pay for it if you do get a judgment? You might be better off making a claim against your own UM insurance.

If you SETTLE with the insurance company (who is negotiating on behalf of the driver), you will be asked to sign a release/settlement agreement BEFORE you receive any money. This agreement will specify that you have agreed to give up ALL right to sue the driver for damages for this accident in exchange for the agreed-upon settlement amount. Thus, if you have settled, you are barred from suing the driver after settlement. If there is any doubt that the policy limits will be high enough to cover all of your damages, you should consult an attorney about filing a lawsuit against the driver and seeing if he/she has assets which might satisfy damages over and above his/her insurance coverage.

On the Bodily Injury question. You may need to bring an "underinsured" motorist claim against your Insurance Company if the limits of coverage for the other car are not adequate to fully compensate you.