It will depend on the airframe but the fire wire or element 'signals's are usually routed back to the FPCU (Fire Protection Control Unit) which is a central unit that detects multiple fire, smoke events on the a/c. If both loops are damaged or the wiring, it is likely that the FPCU will see this as a o/c and detect it as an internal failure not an actual fire event. However, I know of some recent designs that have modified the logic in the FPCU to accomodate rare events like torching flame where in theory the jet could cut booth loops which may supress a fire warning when you don't want it to.
Not sure about the RB211 design but if a fire wire (thermistor) it will depend on the resistance and capcitance in the circuit and how the control units "sees" these parameters.
Just my tuppence worth.