2nd gen Prius - could a misfiring cylinder cause additional shaking / noises when engine turns off?

Title. '06, 94kkm. The engine feels a bit rough at idle but is fine at speed. Feels a lot like ignition coil failure on a previous Toyota of mine. Haven't replaced the coils yet until I can test the current coils. Stranger issue is a stronger-than-normal shudder when the engine stops. Feels like a weight spinning around and then coming to rest over the course of about a second. Sometimes happens, sometimes not. Can coincide with a clunking noise from the transaxle(?). I'm afraid that it might be a bigger issue than just the coil. Chances they're related?

 

I replaced the ignition coils, which fixed the shudder at idle issue as expected. I also replaced the transmission fluid, which I'd been planning to do anyway. The engine/transaxle still shudders when the engine turns off — I'd say maybe half the time...

I'm not totally sure if this is abnormal behaviour for this car, but it is disconcerting.

Thank you for this list of things to check. I've replaced the spark plugs and the air filter. I'll check the intake system next. Not sure how I would check the condition of the cylinders without tearing down the engine — I'd be glad to hear any tips you have.

 

I noticed that the issue is worse when the car is in Drive, but can also happen when the car is in Park.

Anyway, I cleaned the throttle body and shot a can of Seafoam Top Engine Cleaner through. No change.

I finally took the car in to a mechanic and they told me that the top motor/transmission mounts were weak, but didn't recommend replacing them yet as they probably have another couple of years left in them. So mystery solved!