Display Out Of Stock Configuration Option

The decision of whether to show or hide a product based on this setting is implemented
by the Product Price Index.
You can verify this by changing the setting to "Yes" and then viewing a category with an
out of stock product; you see the product is present. If you then change the setting to
"No" and view the category again you will see the out of stock product is still present.
You will also notice that these two indexes now need refreshing:

• Product Attributes (catalog_product_attribute)
• Product Prices (catalog_product_price)

If you then refresh just the "Product Attributes" index, the product is still visible,
if you then refresh the "Product Prices" index, it disappears, thus the "Product Prices"
index is responsible for the implementation of this setting.