The sensor alarm and tamper contacts are
closed when everything is OK.
That means the alarm panel zone input normally reads just the 2k2 terminating resistor, which means the connections are neither shorted or open circuit.
The panel internally has a pull-up resistor on each zone input and reads the voltage at the terminal.
It can calculate the loop resistance from that, so it can differentiate a short circuit, open circuit or correctly terminated loop.
You can add as many more normally closed contacts in series with the alarm loop as you like, and any one being triggered (opening) will cause an alarm, as the overall loop has been broken.
The simplest way would be using four core cable.
Connect red & black to both the original and added PIR, then move the terminating resistor to same position in the new sensor. Use the terminals that was in for the two "loop" wires to the new sensor and connect that as the original one was.
The terminating or end-of-line resistor should always be in the farthest most device on each input, if possible.
This does not show the resistor, but demonstrates the concept:
These are some of the valid possibilities for connecting sensors to alarm zones such as your: