You should be able to do this in a kind of manual way by adding a toggle to your product settings and call it something like “Out of stock”. You can do this on the collection list, and on the actual product page too.
You’re currently not able to show how many of an item is left, unless you update it manually, but this is a great idea however 
Here’s a quick video which I did to try and explain the manual way. Any questions then I’ll be happy to help 
