Your post is a bit misleading, a negative timer preset, or accumulator value will generate a Major Fault, and the processor will shut down, unless you have a fault routine that clears the fault.
You need to be clear on the difference between Minor and Major faults, and the different classes of Major Faults, eg. recoverable, or non-recoverable. Non-recoverable major faults do not execute any "user" fault handling routines, they will cause a processor shutdown immediately, and you will not be able to write tag values with the fault type and code number.
You can't handle recoverable major faults in "normal" code areas, it has to be done in either a program fault routine, or a controller fault routine.
The "description" of faults (by type and code) appears in the programming software "help", and in the on-line manuals, you can, I believe, use these descriptions in your application without copyright issues, but it might be worth checking copyright with RA.
Now, down to basics, recoverable major faults are mostly caused by a bad user program... your code should prevent them happening, don't execute the instructions that cause them. Generate an alarm in your alarm handler to annunciate these occurances. Once the major fault has been triggered, it is usually too late to do anything about it.