Under "Catalog" and the "Inventory" tab, there is a new drop down menu under the "Remove Products from Available Inventory" option. You can now choose to have items removed from inventory at Checkout, instead of the Miva default of "when added to basket."
Normally when you add a product to the cart, it gets removed from inventory until you purchase the item, or your basket expires (typically 60 minutes) and expired baskets are deleted. The new Inventory At Checkout settings allow you to not reduce inventory until the item is actually purchased.
When you select "At Checkout," what happens is, when a customer adds an item to the cart, it isn't removed from inventory until they actually check out and purchase the item, essentially, at the invoice page. This is a nice feature for stores who have low stock or one of a kind items. It allows multiple customers to add an item to their cart without affecting inventory counts.
There is still a check to validate whether or not there is inventory available for the customers purchase during the checkout process. This check happens when the customer submits their customer information (Bill To / Ship To). If there isn't enough items to fulfill the order it will redirect you back to a specific page. You can select which page you want them to be redirected to by clicking the drop down menu under "When Inventory is Unavailable at Checkout."
Here is what the error message the customer will see when their is not enough inventory to cover what is in their basket.