How does Amazon handle out-of-stock situations for products?

If you go out of stock then your BSR will be disturbed so you have to restock ASAP and that also disturbs your IPI.

If you don’t want to drop your ranking then you should always maintain your FBM listing with the same ASIN and whenever you go out-of-stock on that FBA listing you can continue selling on the same FBM listing to avoid any issues in the ranking and indexing.

In this situation, Amazon Private Label sellers can set up automated inventory replenishment systems that help ensure that their products are always in stock. This involves regularly monitoring inventory levels and placing orders for more inventory as needed to avoid running out of stock.