E-Stop and Fuel, software that keeps you awake at night
For modern industrial applications, the safety circuit is often (edit- see child comment's note on safety PLCs) managed by discrete safety relay hardware such as the AB GuardMaster or Pilz PNOZ.  There's a good chance these weren't even available at the time of OP's application!A common configuration involves emergency stops, guard doors, light curtains, etc. being wired in a pair of loops with the relay.  The relay continuously monitors both loops (usually with a phased pulse train), and any interruption or crossover will trip the unit.  Only when the loop states return to nominal will the relay permit a reset to re-enable the outputs.The safety relay's outputs are generally connected to dumb hardware interlocks on the various dangerous bits of the machine.