On BQool, we mark the listings with 0 available quantity as "Inactive" status. 

If the QTY in BQool is 0, you can verify the available quantity in Manage All Inventory page in Seller Central to cross check the data. 

Back order

Back-ordered listings can still be searched in the your Amazon store, but it will take longer for buyers to receive the item after placing an order.

Back-ordered listings will appear as inactive on the Manage Listing page. However, if repricing is enabled, BQool can still reprice them as long as we receive the Price Change Report (SQS).

Out of Stock 

The difference for stockout listings is that those listings can’t be located on the your Amazon store.