The person is a PITA! I wouldn't close the case though I might end the listing in case she pays.
Dear buyer,
I'm sorry you're having financial problems but once you make an offer and it's accepted, you are obligated to pay for it. A listing doesn't have to state how quickly a case will open. In my case, the ebay case opened automatically after (however many days). If you check your ebay messages, you'll see that I sent 2 previous invoices prior to the case automatically opening.
As a seller, there's no "rule" against relisting an item while a case is open. While I do run the risk of someone buying it just prior to your payment, in my experience, that doesn't usually happen. If you contact ebay, they'll tell you that I haven't broken any rules.
If you'd needed extra time to pay, you could have let me know and I'd have waited and made sure the automatic case didn't open but not having heard from you, I assumed you'd changed your mind. If you don't want the item any longer, just don't respond to the case and it'll close on (insert date).
Sincerely,
Seller