The FADEC is not a computer. It is a system.
If you lost the comtrol over the engine or only loose some protections/indications depends on what part of the system fails.
For example the system of the CFM56:
The FADEC (Full Authority Digital Engine Control) system consists of a dual channel
EEC (Engine Electronic Control Unit) and the peripherals that follow:
● Hydromechanical Unit (HMU)
● Dedicated ECU Alternator (PMA)
● VSV and VBV, HPTACC, LPTACC, RACC systems
● Start System
● T/R System
● Oil/Fuel Temperature Control
● Engine Sensors
● Electrical Harness