When a product is deleted on your CMS (prestashop / magento etc...), it is not deleted in Boostmyshop but suffix "_deleted" is added to the sku : 

The product is not automatically deleted to preserve product historical data (orders, purchase orders...) but also stock levels.

What ever CMS you use (Prestashop, shopify, magento etc...), your catalog is synchronized with the feed "Product update" : this feed checks all your products and make sure data in Boostmyshop is up to date.

After this feed is complete, all products imported in Boostmyshop that are not found on your CMS are flagged as "_deleted"

It is important to understand that the link between a product on your CMS and a product in Boostmyshop is based on the product ID, not the reference.

So if you delete a product in your CMS and create it again with the same reference / sku, you will get 2 products in Boostmyshop: 

- One referencing the old product ID, with suffix _deleted

- One for the newly created product, with the sku

If you need to see to what product ID a boostmyshop product is linked to, go within the product view in Boostmyshop and select tab "Integration details" :

As stated above, products are not automatically deleted in Boostmyshop : if you wish to remove them, you can fitler product list with _deleted search and use mass action to delete them :