While I agree with iant's answer with respect to safety devices, there is also another more general answer, too.
Any time you are evaluating the "what-if" scenarios in a system design, you have to determine how you want your system to respond when a sensor fails in either condition (short circuit or open circuit). Iant addressed this in his answer above for the safety devices, however it also applies to normal non-safety devices too. In "most" of these cases you are more interested in how to respond when a wire is broken (open circuit) but you definitely need to evaluate the shorted circuit condition, too. The term "Fail-safe" indicates that such a failure will cause the machine to respond in a favorable fashion (do nothing, stop, stay where it is, shut off the motor, etc.) rather than respond in an unfavorable fashion (motor turns on, motor stays on, valve closes causing extreme pressure, etc.). Frequently there is quite a lot of additional programming required to handle these conditions, but that's all part of it.
As others have said in this forum many, many times, the easy part is figuring out how to make things work the way it should when everything is perfect. The hard part is effectively handling all the break-down situations. This part, and how efficiently and effectively you achieve it, is also the same one that defines you as a programmer.