Keeping guest's bill opened until departure is always highly recommended as it gives you an opportunity, to process possible corrections that might occur during the stay and still providing at the end of the stay neat and clear bill to the guest.

Once guest's bill is closed, from the accounting point of view no changes can be processed to the bill. Therefore, you would need to open new bill, where you can process corrections or even re-post sometimes entire list of the items from the initial bill, that can be quite time-consuming.