The following contains excerpts from eBay's article Using the Out-of-Stock Feature

Common issues when NOT using this feature

If this feature is not enabled, and you are not filtering or ending listings that are out of stock, then you will see the feed fail to update inventory to "0" quantity.

Error message: Quantity is not valid. The quantity must be a valid number greater than 0.

Once you enable the account settings to  “Use the out-of-stock option”, then the feed will be able to update your listings to quantity = "0"

Using the Out-of-Stock Feature to Keep your Listings Alive

When this feature is enabled, it is automatically applied to all the user's existing listings and to any new listings they create. When the quantity of an item goes to zero in a listing using this feature, the item remains 'alive'. When the item is in the out-of-stock state (quantity equals zero), the item will not be shown in the search results until it is back in stock (quantity greater than zero).

To enable the Out-of-Stock Feae, follow these steps:

1. Go to My eBay > Account > Site Preferences
2. Under “Selling Preferences,” click “Show” next to Sell Your Item form and listings
3. Click “Edit” next to “Use the out-of-stock option”
4. Select the checkbox, then click “Apply”

Out-of-Stock Feature Overview

Using the Out Of Stock Control Preference sellers can keep their GTC (Good 'Til Canceled) items alive, even when the quantity goes down to zero. This enables them to replenish stock for the same ItemID, without the need to relist it when the item is back in stock.

This feature is useful for a seller who is waiting for additional stock of an item with the same ItemID. Instead of ending the listing and then recreating it when the inventory arrives, this feature hides the listing from search. Then when more inventory is available, they can update the inventory of the item and the listing would appear again. 

Benefits of This Feature

The following are the benefits of using this feature.

• Saves time because the seller does not have to end and recreate the listing when waiting for additional inventory
• Improves inventory management
  • Due to the 1:1 SKU and ItemID mapping, the seller doesn't have to refer to multiple ItemIDs to get a count of how much they have in stock, what was sold, etc.
  • Since the listing stays alive, the sales history is retained
• Increases SEO (search engine optimization) because the item is long running, which increases the chances that it will be indexed by popular search engines.
• Variations management becomes easier because
• Variations with zero quantity, which do not have sales, are kept alive
• All the variations can have a zero quantity

What Happens When This Feature is Enabled

The following describes how single SKU and multi-SKU items work when a seller enables this feature.

• On a single SKU item and the quantity is zero, the item does not appear in the Search Results page. If a user has the ItemID, they can go to the View Item page directly. On this page, the Buy It Now and Add to cart buttons are gone, and there is a label showing that the item is out of stock.
• On a multi-SKU item and at least one variation has stock, the item will appear on the Search Results page. Variations with zero quantity will be shown as 'out of stock' on the View Item page. When all of the variations have zero quantity, the item will not appear on the Search Results page. However, if a user has the ItemID, they can go to the View Item page directly. In that case, all the variations are grayed out, the Buy It Now and Add to cart buttons are gone, and there is a label showing that the item is out of stock.
• Variations: Changing the quantity to zero of variations behaves differently depending on whether the feature is enabled or disabled. The following shows the behavior when setting the quantity of a variation to zero. In this example there are three variations; A with a quantity of 5, B with a quantity of 3, and C with a quantity of 1 and there have been no sales of any of these variations.

Fees For a Listing With Zero Quantity

When a listing using the Out-of-Stock feature has zero quantity, the listing fees are refunded if the listing is out of stock for the entire billing month. If the listing is out of stock for 3 consecutive billing months, it is ended as shown in the table below.