As far as I know, there is no 'Short Circuit Detection' (SCD) on the diagnostic input modules. There is however, 'Open Circuit Detection' (OCD).
Ken succinctly stated it above, that you really cannot determine a field-wiring short on an input module, but didn't get into the 'Open Circuit Detection'.
Basically, for the diagnostic input modules, OCD must be first enabled in the module, for a specific channel, and then, you put a loading resistor across the field device. Note, that the loading resistor may not be required if the field device is a solid state switch that has some leakage. The module will then be looking at all times for current flow... tiny current = device is open, large current = device is closed, no current = there is an open in the field wiring (or the leakage/loading current is insufficient).
Decent 'burglar alarm' type systems do indeed employ both OCD and SCD, but as stated above, it's a bit more complicated, and requires an input that can resolve 4 states.