You should contact your insurance company and ask them to get involved. They should have obtained a release to protect you from any further claims when they paid out he money. They have a duty to defend you even if you are no longer a customer today.
First off if your insurance paid out they almost certainly received a settlement release precluding any further action - contact your insurance immediately for further handling and request a copy of the release. Second, you can have your license suspended - but there must first be a judgment against you followed by a certification from the court that the matter is auto related. Third if there is a valid release in place the debt collector may be in violation of the fair debt collection act which carries some pretty stiff penalties. Obtain a copy of the release and consult an attorney for any action against the debt collector.
If you were previously sued for the same claim and the party suing did not accept a settlement within your policy limits but chose to get a judgment - and that judgment was for an amount that was greater than your policy limits - then, Yes, that party can take the money from your insurance carrier and seek to collect the balance directly from you. However, if that party entered into a settlement with your insurance carrier, for the same claim of injury/damage now being pursued, and a Release was given in return for the monies paid over by your insurance carrier, then the present attempted collection is improper and should be defended against. Contact your [prior] carrier and advise them of the situation. They are still obligated to defend you, and will at least be able to clarify what they paid out the last time, whether they got a Release, etc. Good luck.
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