OpenCart has the option to show an out-of-stock of warning but will depend on several things:

How to Enable the Show Out-of-Stock Warning in OpenCart 1.5

1. Login to the Administration Dashboard as an Administrator
2. Hover over the menu bar where it says SYSTEM and then click on SETTINGS in the drop-down menu
3. Select the STORE that you wish to edit and then click on EDIT on the far right to proceed
4. Click on the TAB that says OPTION, then scroll down until you see the option labeled SHOW OUT-OF-STOCK WARNING as shown below:
   
   
   
   
5. Select YES to enable the option and NO to disable it. 
6. Click on the blue SAVE button in the top right hand corner of the screen to save your selection

The Show-out-of Stock warning is an option that requires a few things to occur in concert before the warning is actually displayed.  When it is displayed on the store front it will appear as below: