In flight there is a nice smoke effect coming from each of the four engines.  However, the smoke still comes from each engine even if it shut down.  Details below:  
 
1. Product name and version?  C-130X, base pack v1.1 SP1  
2. Download or a box?   Download  
3. MSFS version? FSX Acceleration  
4. MSFS Service Pack version? SP2  
5. What exactly doesn’t work or works wrong? (screenshot required for all graphics related issues)  
When I shut down an engine in flight, smoke is still seen trailing from the shut down engine.
6. When it happens? When in flight, with one or more engines shut down.
7. How exactly do you think it supposed to work?  The manual says you can cruise with two engines, so I like to shut down two engines once at cruise height.  The smoke effects should then only come from engines that are running.
8. What is your system? (OS, video caed , RAM, CPU, Sound Card) Win XP SP2, X1950Pro 512MB, 2GB Ram, 3GHz P4 D CPU, Sound Blaster.  

Maybe this isn't a bug, if the developers haven't tried to model the smoke from each engine.  In that case, this should go in the "nice feature to have in the future" forum.  :)

This is how FSX smoke system works. Basically it does not care if an engine is running or not.