Tira here to help.
It sounds like you want to notify your customers by email only when you've restocked an item. Is that right?
If that is, typically you can notify a customer when an item is back-in-stock with apps from the Shopify App Store. The Shopify App Store contains third-party apps made by third-party developers that help you enhance your store with different features. From my experience, the apps won't notify your customer that an item is back-in-stock until the item is stocked.
You can use an app like Back in Stock: Customer Alerts by SureSwift Capital to set-up an email notification to your customers. Customers would receive an email when the item is back in stock, and with a link to help them purchase the item. As this app is developed by a third party developer, you can reach out to the third party developer for support by using the information listed under the "Support" section of the apps page. We also have a list of similar apps here: Back in stock apps.
Have you tried this process before, where the customer received an email after asking about a back-in-stock product?
No, we do not want to notify our customers when we've restocked.
Instead, we want our customers to notify us when they want an out-of-stock product to come back.
For example: There is 0 stock of a baseball bat that has not been selling well. If 5 customers want it to come back, we would like to know that they want it to come back. This way, we will also know how much quantity to restock.
Thanks for confirming what you're looking to do, @AVW.
If you want customers to let you know if they would like a product back in stock, one option I would suggest is to replace your "add to cart" button with a link to contact you to let you know that they would like to see the product.
If you're using a free Shopify theme, you can follow the steps to make this customization in your theme's code included in this guide: Replace "Add to Cart" button with a contact link.
If you are using a theme that you purchased in our Theme Store, then you may want to reach out to the theme developer to ask them how you can customize this feature into your theme as these themes are made by third-party theme developers. I recommend passing along the help doc I suggested to them so that they can see what you're looking to do and offer guidance.
Check out where to find support for your theme from our help docs, here.
Do you have a link to an example product that hasn't been selling well? I would love to provide you with some suggestions on how we can help you improve your sales for the product.