Advise extension which can do: buyers can order products even if they are out of stock !
Go to Solution.
It is possible in Magento if the product has quantity 0, but is in stock. If it is out of stock, Magento will not show add to cart button and will not let the customer buy the product.
Then you need to set up 'Allows backorders' option in Inventory tab of products edit form -
Then when person adds this product to cart, the notification will appear -