1. Show out of stock products in Magento
A. Login to Magento backend
B. Take menu System-Configuration.
C. Take inventory tab from the left panel
D. Set Display out of stock products to ‘Yes’ in Stock options tab in the right panel
Now you can get see your products in front end, even if the items are ‘Out of stock’.
2. How to hide products on Magento store that are "Out of stock" or have a QTY of 0
Hide out of stock message is a configurable item.
Admin >> System >> Configuration >> Catalog >> Inventory >> Stock Options
Display Out of Stock product -> No