The EECs controlling the Airbus engines, and Boeing's too, have dedicated generators which will provide all the power you need to receive control data as long as the engine is running. This creates the shut-down problem in the first place as if no cockpit signal is received the engine will carry on at last commanded value until the fuel runs out or it gets flamed-out some other way.
Thanks for the picture, Mechta.
I remember this being immortalised in the Gooney Bird song "One wing askew, and yet she flew, the DC two and a half. ..." but never had any real evidence!
VnV