I am not sure about how a Benz works in this fashion, but in some cars the cores are vented when the engine looses vacuum. This is so they can "air-out" and prevent this problem. Since you have no air to the outer vents, I wonder if there is a larger problem that is preventing fresh air from entering, either at all times of when shutdown.

Just a random theory based on my limited HVAC knowledge.

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1991 560 SEL / 185k miles
1992 750il / 17k miles - project car