Does the Hadith: "My nation has been absolved of..." apply to a car accident caused by someone who cannot afford the repair costs?

The aforementioned Hadith indicates the removal of sin from you, not the nullification of the car owner's right. Therefore, you are obligated to guarantee what you have damaged of the car. If you are unable to pay the amount, then ask the owner to forgive part or all of the amount. Otherwise, it remains a debt upon you until you are able to repay it.