Immobilizer relies on a signal from the ignition key. Having accepted the signal it sends a OK signal to the ECU. All the other stuff may set the alarm off but won't cause an immobilization.
The above relationship between key, immobilizer and ECU why they need to either reprogrammed or replaced as a set but also why the ECU can be modified to not need the signal and allow the elimination of the immobilizer unit and the key and switch.
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