To show an out of stock item in your store, you should set the Back Order Option.
The Out of Stock Image display option is a simple replacement of the Buy button found on a product page. Since there's no Buy button, customers will not be able to put the item into their shopping cart. However, if they have added the item to their cart before the Out of Stock Image was updated, they will still be able to proceed to checkout with that item.
If the price changes or is out of stock for an item that is in a customer's shopping cart, it is updated as you might expect; the new price will be reflected in the cart.