QuarticOn customer's panel make it possible for you to decide whether the search results should also contain products that are not available. By default, this option is disabled, but you can enable it yourself. How?
1. After logging in to https://cp.quarticon.com/ go to the AI Smart Search panel by clicking Search in the menu on the left.
2. In the AI Smart Search customer's panel go to the Settings tab.
3. Check the box right next to Show unavailable products in the General section.
4. Confirm changes by clicking Save settings.
From now on, unavailable products will appear in search results.