This is definitely the most common and well known superstition in Korea.
From the tittle you are probably wondering about: "what the heck is a fan death?" Well it definitely not when your bias is freaking killing you with the perfection and their hot self and then there you have it a fan death. 
No, it's simply a regular fan that keeps you cool in the summer.
It is said in Korea for anyone not to leave their fan on during the night, for it will kill you.
When I first heard this I was just how can a fan kill you it has no legs or arms it's not like it's gonna come at me and freaking choke me right? 
Well I got to say this superstition is probably the most truthful one I can say. Not by much but it is. 
Anyways, the reason for this is that: if you leave your fan on at night it can cut off the circulation around you especially if you are sleeping in a very very small and tight room. Of course that's not the only reason.
Another one is simply because if even if it's summer and you are in a tight and small room with the fan on, and it's really hot, but the only thing that's keeping you cool is that oh so cool fan.... it can possibly kill you, how? Well if it's cold enough and close to your face you can possibly get frostbite off of it. And that's why if you were to ever got to a Korean person's house you decide to keep that fan on at night there is a big percentage that they will warn you not to keep it on while you sleep.