In the filters tab of the app we have the option to import products with zero stock. This setting only applies when uploading products, helping to prioritize loading only products with inventory, and excluding out of stock products until they come back in stock. At this point they would then be imported.
"Import products with zero stock"
We don't remove products based on inventory levels, because if we removed a product everytime it went out of stock, and then added it back that would be to many products being deleted and reloaded. This can hurt SEO, mess with links people save, and generally create a lot more products to import which would slow down the process of loading all the products that match your filters.
If you are getting lots of orders for out of stock products, there's a few things you can do. There is a setting in Shopify called "continue selling when out of stock". You may want to disable this setting.
This Shopify help article explains how to hide out of stock products.
This is our article on continue selling when out of stock.