Shopping Feed keeps each of your channels inventory up to date based on the count in your storefront. When a sale occurs on one of your marketplace channels, this changes the channel's inventory count. Shopping Feed accepts the new inventory count and updates your storefront inventory accordingly. Then, this new inventory count is updated across all your channels.
In the case where a product sells out on one of your channels, Shopping Feed removes the product from all other channels, until inventory is available again.
Put more simply: When the inventory changes on any of your channels or your source feed, Shopping Feed changes it everywhere else.