But the requirement is that the LED light up when there is NO signal, that is, the voltage level from the barrier strip is zero. And I think we are to assume that no microprocessor is used or desired.
What then will power the LED? There has to be a power source for the LED that is separate from the barrier strip signal, that is, stays ON when the barrier strip signal goes low. Then a P-channel mosfet in a highside switch arrangement can be used.