Sinking Digital Input Module

A "sinking" input module sinks current to ground, which means the 0 or N24 power supply terminal connects to the "Common" terminal on the module, and the P24 or (+) terminal of the power supply is distributed in the field.

To see an example of this, download this Allen-Bradley PLC I/O module manual and look at the example wiring for the 1756-IB16 sinking input module on page 146:

http://literature.rockwellautomation.com/idc/groups/literature/documents/um/1756-um058_-en-p.pdf

As you can see, the (-) side of the power supply connects to the "GND" terminals on the module, while the (+) of the power supply goes to the common sides of the field switches.

If your field switches have N24 (-) distributed to them, then the module you need in your PLC is a "sourcing" module where the common terminal(s) on the module connect to the P24 (+) terminal of the DC power supply. An example of this for you to see is the Allen-Bradley 1756-IV16 sourcing DC input module on page 173 of the same document.

In answer to your general question of what happens if one of the power supply bus wires opens and the field wiring goes to earth ground, that all depends on how solidly one of the power supply's terminals has been grounded itself. In most cases, the PLC will fail to receive a signal from the field device if this happens, but the details of your particular installation are what matter to you.