Automatically Unpublish Product in Shopify by Using
Arigato Automation

The automation is fired every time a product is updated. If the inventory level goes below zero, the workflow unpublished the product setting the status to draft. When the product is restocked, the workflow fires and publishes the product.

This automation checks for a product when it's sold out. Waits for 30 days, and if the product is still out of stock, it unpublishes and archives the product.

If you don't want to show products you don't have in stock, this workflow is for you. When it comes back in stock, the product will reappear in your store.