Sounds like the person you hit used the PIP (Personal Injury Protection) portion of their car insurance to seek medical treatment for their injuries. PIP pays up to $15,000 of medical treatment during the first year after the accident. The insurance company will typically then go after the liable party for reimbursement. If you had insurance your insurance would have scrutinized the bill and paid what was reasonable related to the accident. (Just because the PIP paid it doesn't always mean that the charges are related to the accident although they are supposed to be related for PIP to pay them. Sometimes people take advantage and get treatment beyond what the accident caused. But it could also be legitimate treatment and you just didn't realize that this person had more symptoms then you thought initially. It is quite possible to have a lot of neck irritation from whiplash that lasts a few month and people often run up bills getting chiropractic treatment.
You should also be aware that the bill you are being asked to pay is only the tip of the iceberg. You are very likely to be getting notified by an attorney for this person sometime in the future that in addition to the reimbursement for out of pocket costs for PIP that you are being presented with from the insurance company, the person via an attorney wants more money for pain and suffering. So don't think negotiating a settlement with the insurance company will end this mess - it probably won't.
Your only option is to pay money - either the full amount they are asking or some amount that is agreed on with the condition that the injured party sign a release so you are not facing any future claims. The insurance company doesn't have to negotiate with you and may not be able to promise you a release.
At some point either the insurance company or the person injured will file a lawsuit. Depending on what strategy they use, they might also ask you to pay their attorney fees so the bill can get even bigger. You will need to hire an attorney to help you through this mess. If you have limited funds then you might have to consider filing bankruptcy. Bankruptcy is the cheapest way out of the problem - you may pay around $2,000 in total and never have to worry about paying any more to end these claims. Bankruptcy might also get you out of paying other debts you have. But bankruptcy is not for everyone and you really need to talk to an attorney before you consider this as an option since you want to make sure you don't risk loosing property or investments you have if any. (Of course if you have property or investments you might be in a better position to negotiate a settlement with both the insurance company and the injured person.)
Also be aware that if they proceed to court and get a judgment against you, the State of Oregon if asked by them, can suspend your driver's license until the judgment is paid. (This is only when a judgment involves damages from an auto accident.) A bankruptcy or settlement will prevent you from suffering a license suspension as well. http://www.portlandlegalservices.com
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Well this is definitely a "bad facts" scenario. You don't mention how long ago the accident occurred, but you were uninsured when it happened. That is the essence of the problem of course. When you purchase insurance, there are really (at least) two primary coverages -- payment for your liabilities and payment for your legal defense. Since there was no insurance in force you don't have coverage for either liabilities or for your legal defense.
There are several options available, none are going to be particularly palatable for you. You don't say exactly what the "claim" consists of -- a letter from the insurance company, a call from an attorney, a summons and complaint or a judgment. The progress of the claim through the claims process and litigation process is important in determining the best course of action.
First, it may be possible for you to work out a settlement agreement with the other driver (or his/her insurance company) to make periodic payments to pay their expenses incurred in the accident.
Second, you could hire an attorney and pay out of pocket for that attorney to fight with the insurance company and/or other driver on the issues of liability (whether you owe anything) and damages (how much you owe).
Third, if you have been served with legal papers you will almost certainly need to hire an attorney (again, likely paying our of pocket) to defend you from the other driver's claim.
Fourth, if there has already been a judgment taken against you it might be possible to discharge that judgment in bankruptcy. This is most definitely a step which should only be considered with expert help from a bankruptcy attorney. As a non-native it may not be possible for you to even ask for a discharge in bankruptcy, an issue on which I am not qualified to comment.
You should consult with an attorney. With a more complete recitation of the facts it might be possible to find a more palatable option. Good luck!
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