The Gift Box app takes the information from your store and displays it accordingly. It means it will show information based on your store's real-time data.
If one of the products that you have chosen as a gift for your customers goes out of stock while the offer is active, Gift Box won’t show it in the application unless the product has the “Continue selling when out of stock” option is enabled.
To enable/disable the option, in your store's Shopify admin you will need to go to the product page and scroll down to the Inventory section. From there, you can mark or unmark the checkbox, according to your preferences:
Please also note that when you are creating a new gift offer with out of stock products, the application will display a message to let you know the product is not available:
The application will allow you to Save and Activate the Gift, however, it won’t show up on your store.