The fan is on a thermostat, causing the fan to run if cooling is required, even when the car ignition is turned off. Having said that, if you notice that the fan is running long after you've shut the engine off, you may have a problem!
Its not your engine. Its the fan running to cool the engine down. They all do it and nothing is wrong with your car.
Economy mode should only come on after half a hour of the ignition being on with the engine off. The windows and radio should still be able to be used when the engine is not running. If this is happening other times check your battery.
if its the key card type, it may be the ignition relay, which is locatatd by the acclerator pedal under the dash, it is the black larger relay. with the ignition off and the engine still running give this relay a tap, car should cut out. i speak from experience as this was happening to my laguna.
It sounds like your dizzy cap isn't lined right which causes the engine to stay running after the ignition has been switched off. i had the same problem with my fiesta
If the check engine light is flashing when the engine is running , that indicates that an ignition misfire has been detected
Sounds like the engine heats and the ignition fails.
subaru legacy engine is switched off when stop after drive
My first guess is that your ignition switch has gone bad, but if you have done work on the engine recently recheck your wiring.
Sounds like you are loesing the live for the radio when the engine is running cheak the ignition barrel is ok Just an idea Oliver
subaru turbos do that to
Faulty ignition switch.
Fuel pump