They can file suit in the state you live, however what will most likely happen is they will sell the debt to a debt collector and write off the loss. Then they will report you to the credit reporting agencies as R-9 write off (that's very bad for your credit rating!). The debt collector will also report the R-9 to credit reporting agencies to hit your credit rating 2x with the same debt. And that debt collector will charge you for their services... say 2x the original debt. A $1000 debt suddenly gets reported to the credit bureau as a $2000 debt.
Depending on where you live, the debt collector has a limited time to get you to pay up. Maybe 3-5 years. So they will contact you, demand payment and offer a settlement. If you accept that settlement, you've just admitted to owing the debt to the debt collector and they can pursue you for the rest. In court. You might be threatened, you might receive constant phone calls and constant letters to you (and maybe your family) and a whole slew of other illegal activities. Make sure you download an app to record your phone calls. There are plenty out there. When they call you and say "you're on a recorded line" you respond with "I'm recording it from my end as well".
Anyway, you can demand the debt collect cease contact with you and provide proof of debt (you have to do that in writing - and I'd open a PO box for all communication if I were you). If they don't provide proof of debt, you send another letter and let them know any further contact is in violation of the fair debt collection practice and has a liability of $1000 per action. And let the debt collector sue you if they can.
Meantime, you should know, the debt collectors might report their entire inflated bill (that $2000 bill) as taxable income to the IRS. That's their latest scam to get you to pay. In which case, you might owe say $600 in taxes that gets penalized and fined until you pay it or present a case to the IRS.
If the IRS decides you owe that $, they can report it to the credit bureaus as a tax lien (another bad mark on your credit rating) and they have 10 years to collect.
my suggestion. Contact the credit card company and work out a payment plan.