I only have limited information regarding the matter. Not sure if insurance denied coverage and I am not sure why. Start by contacting your insurance and getting a copy of the last EOB. Appeal the EOB with the insurance company. There are internal appeal procedures. Keep that voicemail. There may be an issue with bad faith by the insurance company if they agreed to a certain payment and then refused to pay it or if they are acting in bad faith. However, take the necessary appeal steps. Sometimes I find that when a matter is internally appealed, the issue is resolved. If the hospital sues, you can also bring in your insurance company as a party and bring a bad faith action against your insurance company (assuming they did act in bad faith).
The answer above is only based upon the limited information provided. The answer is limited and my review is likewise limited, and thus the response is not intended to be acted upon as legal advice. Although licensed in numerous states, I am currently only licensed to practice law in the state of Nevada. No attorney-client relationship is formed until you sign an attorney-client agreement with my office. Any information provided is for discussion purposes only and there is no attorney-client relationship formed. Only general legal information is provided. Each case is unique and accurate legal advise would require review of all details and documents for each specific case. It is possible that the comments here, while meant to be helpful, may in some cases not be complete or accurate.
Most such debt can be successfully negotiated.
And for most people, such debt is large enough to at least seriously consider bankruptcy (which I've added to the question topics).
My office handles both solutions, and can usually get you an appointment in a day or so.