The availability of the storefront listings of items, which have 0 stock or vendor stock is being controlled on item level by the Availability field in the UI or by the particular values, that are set/selected in the corresponding rule and state bulk headers.
You would be able to download a spreadsheet of all of the bulk headers and acceptable values from this link and there are 3 valid combinations of the values in the rule and state headers, which basically represent the Availability field in the UI and please see the details and screenshots below:
- update + active corresponds to Always Available - Always Display in the UI and the particular item would be always available for purchase even if it has 0 stock
- update + stock corresponds to Inventory Controlled - Always Display in the UI and the item's storefront listing would be accessible, but an Out of Stock notification would be displayed
- end + stock corresponds to Inventory Controlled - Disable When Unavailable in the UI and the item's listing would be disabled when it reaches 0 stock and it wouldn't be accessible anymore