I had a credit card canceled once, when the credit card company decided to quit issuing cards to people with Illinois mailing addresses. They sent me a letter six months or so in advance that said, basically, "You can go on using your card until it expires, but you're not getting another one, and be sure to change any automatic charges before the expiry date. You can go on paying the balance according to current terms." If I'd been insane, I could have drawn on the card up to the credit limit, right up to the day it expired, but charges after that would have been declined.

The most likely scenario for a HELOC would be just to tell you that you couldn't draw on the line of credit. (As you suggest, essentially dropping the maximum down to your current balance, and then tracking the balance down as you pay off the amount owing.) They could sell the debt, but they wouldn't need to--they could just switch to simply servicing the existing debt as if it were a plain old loan and not a line of credit.

I'm sure if you read the terms of the loan you'll find that they can change the terms anyway they want and that you still have to pay the money back. (If you don't borrow any new money, you can usually pay the money back under the old terms, but you still have to pay it back.) And I'm sure the terms allow them to stop lending you new money for any reason at all.