I hadn’t heard about this before. But I guess it’s a well-known truism. PRI even did a report on the belief in Korea that leaving a fan on overnight could cause death and many fans in Korea have timers to make sure no one forgets before going to sleep.
As PRI says, “A number of websites espouse theories about the origins of fan death. One way Koreans believe your fan can kill you is hypothermia. As the theory goes, if there’s a fan blowing all night, it may cause your body temperature to cool down enough to cause death.
They also worry about suffocation: that a fan left on in a sealed room just circulates the heat and prevents proper breathing. There’s even a theory that the South Korean government concocted the idea fan death to persuade citizens to decrease electrical use during an energy crisis in the ’70s. Of course, there’s no evidence to support any of these theories.”
Of course, even more popular is the idea that putting ice in your drinks during hot weather will make you sick or give you a cold. A popular belief that almost every traveler to hot regions has heard. Or don’t swim right after you eat. In China, it’s widely believed that sitting on a seat recently warmed by someone else can give you hemorrhoids.
According to Wikipedia, “Fan death is the belief that death can be caused by sleeping in a closed room containing a running electric fan, due to the risks of nausea, asphyxiation, and facial paralysis from the technology.  . There are no verified cases of the alleged phenomenon, but it remains a widely believed urban legend in South Korea.”
Even in the USA, virtually all Korean kids have heard their parents say, “Don’t leave your fan on all night.”
We found that the American Environmental Protection Agency (EPA) actually discourages people from using fans in closed rooms without ventilation during excessive heat, specifically when the heat index is above 99 °F (37 °C). But not due to fears of fan death.
Slate reports that it is also a Slavic thing and that Russians have been known to believe the same thing.
Ken Jennings actually grew up as a child in Seoul, South Korea, and fans were no laughing matter. Everyone took the Great Fan Menace for granted and had a hard time believing that other cultures were ignorant of it. (http://www.slate.com/articles/life/foreigners/2013/01/fan_death_korean_moms_think_that_your_electric_fan_will_kill_you.html)
Still confused? Here’s the EPA’s actual statement regarding excessive heat:
For all that, if moving to Korea, or if you are a Korean living in America (or elsewhere), what you do behind closed doors is your own business. Run the fan, turn off the fan, it’s nobody’s business but your own. Just make sure you have a good policy first.