Sparq Search auto-detects stock quantity of products and hides these products automatically in the search results. Your customers can see these products when they choose “Include Out of Stock” from the availability filters.

You can also control the visibility of your store products using the "Hide Out of Stock Items" option, which utilizes the default Shopify out-of-stock inventory model. You can visit the URL and update the setting as shown in the following screenshot,

Once enabled, it will hide items for which Shopify reports out-of-stock quantity.

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