I reread your post and I believe your setup is.
An alarm console with a motion sensor input.
On the sensor end is a 2K resistor that I believe gets shorted out on a trigger. If it is in series as you suspect then I would say the sensor opens whan triggered. If the resistance of the wiring back to the console breaks or gets poor. The resistance gets higher than 2K or the loop goes open. That then triggers a open wiring trouble report.
Did you connect I1 and I2 across where the motion sensor ties to the console or in series where you removd one of the original wires to the console. Then connected the loos wire to I1 and I2 to the original terminal where the sensor was connected.