It appears you are asking about a subrogation right with your own health insurance company. You need to look at the contract between your health insurance and you in order to determine if they will reduce their lien so that you are able to put money in your pocket.
I would encourage you to discuss this with a lawyer in your area who does personal injury plaintiffs work, so you don't compromise your claim.
Before you sign anything...contact a lawyer...
Good luck...
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