In order to be sure that out-of-stock products aren't visible to potential customers, you need to change your inventory settings in your Shopify account.
1. First, make sure that tracking is enabled on your products in Shopify. Click here for more information.
To do so, go to the inventory section of your products, click the Inventory Policy dropdown menu and choose Shopify tracks this product's inventory.
2. Next, you need to make sure that you change the automated collection conditions for your products. You can learn more about automated collections here.
- For Products must match, select all conditions.
- For Inventory stock, select is greater than and 0.
This will assure that your automated collections don't contain any products that aren't in stock, and therefore those products won't be visible to customers. Any out-of-stock products will appear in your collections again after you've received more inventory.