If you use NetSuite for your webstore, I believe there's an Out Of Stock Behavior field on the item record ( it may be hidden, depending on your item layout ), but it's a drop down menu, and you can select to 'Remove item when out-of-stock' and it will remove the item from your website as soon as the stock hits 0. You can set the reorder point and such to 0 as well so once it won't show up on the reorder screen. You can also create a saved search that sends you an e-mail once it reaches 0 so you can make the product inactive