When a product is out of stock, you have two options:
You can hide it or set it as sold out via the Availability manager.
This is the way we recommend you to do it.
More info on how to this via this article.You can either hide it or set it as sold out via your menu. This article covers this option
A. Mark a product as sold out via your menu
The product is still visible on the menu but not selectable.
Go in the orderBilly backoffice to 'Menus' and select the menu on which you'd like to modify the product status. You can click on the 
or the ✅:
- means it is out of stock; you will also see OUT OF STOCK next to the icon.
✅ means it is in stock.
Your changes are saved straight away, without having to click on 'Save' in the top right.
This is how it will appear on the menu for your clients:
Hide a product via your menu
You can temporarily remove a product from your menu by hiding it. To do this, go to the orderBilly back office and navigate to ‘Menus’. Select the menu you want to update, then click the eye icon next to the product to make it invisible.
Also here, your changes are saved straight away, without having to click on 'Save' in the top right.
The product will no longer appear on the menu for your guests.
IMPORTANT NOTES
Changes made within a category (product order, sold out status, hidden products) apply to every menu that category is linked to. If you want to manage a category independently per menu, create separate categories that are each linked to only one menu.
Changes made by one user will also impact what another user sees: the changes will also be visible for the other user. Not sure if you are working on the latest version of your menu? Reload the page in your browser before editing; now, you are certainly fine.