Hey Dustin,
the VFD and the CNC controller have to be wired in a way that they are part of the emergency stop circuit. The VFD should signal an alarm to the CNC controller if there is a problem with the spindle (not) running, which then will stop the running g-code program, but also should the VFD stop the spindle when there is an alarm of any kind, be it from CNC controller, or from something else, e.g. if someone opens the door of the CNC machine’s enclosure etc. For this, there exist dedicated Safety relays and sophisticated emergency circuits.
I tried to make my best to answer this question in this forum in the past:
E.g. you could have found this posting.