Ultimately they can sue you for the amount that you don't pay. Insurance in this regard is a reimbursement, or a "pay through" situation, in that the insurance company gives you the money to pay to the medical service. Most of the time it's paid directly to the medical service, but there are exceptions.
An insurance company is a "third party" payer. You contract
with the medical service to provide a service, and you're responsible for the bill. An insurance company says that they will pay the bill, and like I said, they generally just pay the service, not you. When they do pay you the check, rather than the service, sometimes it's because of other expenses not billed by the service, (for instance payments for pain, suffering, rehab, in home medical devices, etc...) are included all in the same check.
In short, you're going to be responsible for getting that bill handled. They can treat it as a debt against you, and sue you for it.
Now MOST LIKELY, they will contact you in house, trying to resolve it without going to court, and then maybe will send it to a collections agency, to try to collect. You can try to enter into an agreement with them, or the collections agency, to pay out over a period of time. If you can come to an arrangement, it doesn't have to go to court. But depending on the amount owed, it might go to court.
Since the insurance company has already paid, they almost certainly won't get involved. They'll say that their obligations have been fulfilled, so the issue is between you and the medical service.
Again, they'll likely work with you, even agreeing to a payment plan. The key is to try to work something out with them, and be reasonable as to what you can offer and when.
Hope that clears things up a bit. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for my answer unless and until you rate it a 3, 4, 5 (good or better). Thank you, ***** ***** luck to you!