Im not really an expert but from what I understand is that a Fault Model is a 'model' of whta could go wrong in a system. In this case, chips. So, for the multitude of possibilities that things could go wrong, there are a lot of fault models for vlsi.
Single stuck-at faults
Transistor open and short faults
PLA faults (stuck-at, cross-point, bridging)
Functional faults (processors)
Delay faults (transition, path)
and many more. I suggest to read up on these materials if you want to learn more about each of them.