If the battery went dead or the electronics died in the key fob the active low-power transmitter likely wouldn't work (i.e. you wouldn't be able to leave the key in your pocket and start the car) but the passive, backup RFID-type chip doesn't require any power from the key fob battery and appears to be a separate chip.

2006 Ford Focus trunk unlock, from inside the car, no keys, no remote, no breaking of plastic pieces, no broken knuckles, no fuss, no muss.
The all-electric F-150 ® Lightning ™ is equipped with tons of exciting features, including the Mega Power Frunk – a trunk built into the front of the truck. Easy access. You can open the Mega Power Frunk using: Your key fob; The grille-mounted release button; The FordPass ® App; The SecuriCode ® Keyless entry Keypad FORD FIESTA FOCUS ST Dead Battery How to Open Unlock Car MK7 ST Check out our Amazon store for the tools that we use in our videos:
To open the door of your Ford F 150 that has no more battery, you will have to turn the key in the lock and at the same time try to pull the door handle . Repeat this operation if it doesn’t work on the first door on the second one, if it still doesn’t work, go to the next step of this content.
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how to open ford focus trunk with dead battery