Line monitoring is detection of a break or a short.
EDIT: OK actually four states:
* Open contact
* Closed contact
* Open wiring
* Shorted wiring
I've seen this is done with a two-resistor network, one in parallel with the contact and on in series with the contact. The input itself is really an analog input that detects the four different voltage states via the resistor network.
Hope the nickel-tour explanation makes some sense.