A 1746-IB16 input module has its common terminal tied to ground, and receives "a more positive" signal (+10 to +30vdc) to indicate an "ON" condition. So with a positive ground, if an input wire touches ground, the input point in the card will go true.
Be wary of the terms sinking and sourcing and carefully determine what those occasionally mis-used terms are in refrence to.
I would definitely want to know what type of sensors (NPN, or PNP) are to be connected and the loads also.
You will wnat to draw up some example circuits and scrutinize what will happen when an input wire shorts to ground, and how that fits the application.
Do you want a false input? Or do you want to blow a fuse or fault a DC power supply?
There are tons of posts on the subject, and many experts wathcing new ones, so you may get the best answer just by expanding on what is specified in the ciruits vs. what you must design, and a little more about the application.
Paul