As in all electrical devices the circuit breaker is part of the safety system. It insures that if there is a short downstream of the breaker or a sudden spike in amperage, it will trip and prevent further damage to any equipment or wiring downstream. Sometimes facilities use fusible disconnects to perform this same function.
Personal safety is provided by having a direct ground on the secondary or a ground reactor or other device as described by ANSI/AWS Z 49.1 Section 12.4.6
Reference: RWMA - Resistance Welding Manual 4th Edition
ANSI/AWS Standard Z49.1 Safety in Welding