What happens if I don’t pay $65k medical bills?

I had a baby a year ago and had around $200,000 in medical bills immediately after. It was a pain in the ass to get insurance to cover any of it, I kept getting letters sent back saying that it was denied. The problem was because at the time I was under my dads family insurance plan (which we didn’t realize) and on my husbands plan so each company wanted the other to pay and it kept going back and forth. Well, I’ve been recently getting letters for a remaining bill of $65,000 that shows no insurance coverage, I’ve tried calling a few times but it seems like neither side wants to pay for it and since one of the plans is now expired that’s been making it really difficult. What happens if I just don’t pay it? I know it’ll go to collections, I’m just worried about the hospital or collection agency suing me. Is that a thing? I’m so tired of calling and calling with no one helping me, I’ve been fighting this for over a year