I've only seen one engine seized on the MKV before and that was terminal. It had an oil starvation issue to the turbo, which in turn quickly launched the compressor wheel into the engine which in turn caused the internal cam chain to destroy itself and goodbye engine.
If only one cam is turning it is likely that the internal cam chain has broken, lodging itself against on cam and leaving the other free.
Only a hypothesis at the moment, but it doesn't sound good if one camshaft is seized.