I've just closed a non payment case yesterday. It has to be open for 4 days, if you don't receive payment in those 4 days, you can close the case and you get your listing fees credited and the buyer receives a unpaid item strike. Neither of you can leave feedback as the transaction was never completed.
When you are listing items, make sure you set up buyer requirements before hand, this will stop anyone who has unpaid item strikes against their name from bidding on your items.