There are two settings here, and it's recommended that both options are left un-selected, as pictured below. The option selected here will apply to all shops on the instance. Users cannot customise these settings for their individual shops.
Show out-of-stock products:
Deselect this so that when an item is out of stock it no longer shows in the shopfront
Deselect this so that when a product’s stock level reaches zero customers will not be able to purchase the item. If this option is selected customers will be able to continue ordering a product after the stock level is at zero (will go to -1, -2 etc).