By default, out of stock products remain visible but have are greyed and crossed out.
You can optionally hide your out of stock products from your web, embed, and print menus by going to your Menu > ⚙️ Settings and toggling "Show out of stock items".
Out of stock items on Displays always remain visible but are greyed and crossed out. They can be removed or replaced at any time by editing the Display.
Archiving products
If you're looking to archive products, see: How do I archive a product?