Coming back to the original topic, the answer is: depending on type. While most aircraft with FADEC engines do stop if both channels are dead, I know of at least one aircraft, the Avro RJ series, where they have one FADEC and one backup mode.
Not sure you could call the RJ a proper FADEC though ?
Intelligent ECU/EEC maybe. It's a bit of a hybrid as it was basically an upgraded mechanical linkage system from the 146 done on the cheap
Why does that not surprise me from BAe