This could be 1 of 2 things.
You could have a problem with Pre-Ignition - Over run, which can lead to Catastrophic Engine Failure if not resolved quickly.
Or...
This could just be a Turbo Timer which is designed to keep the engine running after you take out your key for a set amount of time (usually 1-2 minutes) to enable your turbo/s to cool down slowly and properly, otherwise, if it/they cooled down too quickly the heat could crack an impeller blade or even cause damage to the impeller bearings. And that would not be cheap to repair.
Most Turbo's are either Water or Oil cooled so by letting the engine run longer once used, it allows the fluid (Oil/Water) to cool and relax the turbo/s before switching off.
If this is the case, then you don't have to wait for the engine to shut off just lock it up and carry on with whatever you are doing.
Hope this helps
Headlights run off the battery not the ignition...
Faulty ignition switch.
Possible switch or lock cylinder
Its not your engine. Its the fan running to cool the engine down. They all do it and nothing is wrong with your car.
Keep the key in the ignition, stupid...
sounds like the ignition switch is bad replace it
A malfunctioning the ignition switch will allow the car to keep running after the key is turned off. You can remove the positive ground cable from the battery to shut the car off.
When any car idles, it lowers the ignition energy (but not completely) to keep the car running. When it is cold outside, your Subaru's ignition energy is lost through heat because electricity also is measured through heat. When there is less ignition energy when it is already running on a lower ignition level, the car (your Subaru) is not likely to idle.
because gas was burn after the spark plug created the spark to burn gas and keep car running.
sounds like the ignition control module
It might but keep a close eye on it.
Coolers are necessary after a turbo-charge to help in the smooth running of the engine. The main purpose of the coolers is to cool down the engine after using a turbo charger.