hi,
The BLUE trace represents the relay contact closures of the detector relay.
I have shown 3 short pulses, that could be caused by leaves or birds breaking the beam.
You can see, during each pulse the timing capacitor of 555/1 charges a little, on the 3rd pulse the cap voltage is sufficient to allow 555/1 to time out.
The low going output pulse of 555/1 triggers the 555/2 input, as the 555/2 is configured as a mono its output will go high for the time of Res/Cap values.
In the case where the beam is broken for a longer period, the 555/1 cap will charge faster and trigger the 555/2.
When the 555/2 is timing it discharges the timing cap of 555/1, getting ready for any further beam breaks.
If the 555/1 see's say, just one leaf, then the charge on the 555/1 timing cap will be slowly discharged by the resistor in parallel with transistor.
You may have to adjust the timing values on the 555/1 to suit the application.
Do you follow OK.?
EDIT:
added a second waveform, showing when detector relay is closed by intruder.
Longer closure time.