One of PSU design concept is to protect the system and take out the chassis residual thermal through PSU fan.
Hence, while AC power cord plug in, the fan will connect to 5VSB and operating slowly; once the PSU triggered the system, the fan will switch to 12V and operating fast.
So, unless the AC power cord is un-plugged, the fan won't stop as the design is it; but we won't prefer this way, because if the fan stop suddenly while system just off, the residual thermal will keep inside of the thin chassis.