No, that's not correct.
The statute of limitations applies to the filing of a lawsuit.
A creditor could conceivably continue dunning you for the debt for the rest of your life but just isn't likely to win a lawsuit after the 6 years are up unless you ignore the lawsuit and the creditor gets a default judgment. That can happen because the statute of limitations has to be raised as an affirmative defense. If it isn't raised, the creditor can theoretically win the lawsuit at any time after the six years are up.
I'm sure they have lots of options. None of them pleasant.
Yes.
But it would only remain on your credit report for the balance of 7 years from the date of default which could, theoretically, be 7 years from now. If they never sent you the bill then it was never in default until now.
Yes.
It's called "dunning" and it's perfectly legal.
Yes.
They would have to win a lawsuit and get a judgment. Then the judgment can be recorded and become a lien for the life of the judgment.
My advice:
Check your records quickly. If you owe it, pay it. If you already paid it, provide appropriate documentation within the 30 days that it's on hold.
Trust me, you'll be a lot less happy later if you try to screw them out of the money.

