Same rules as climbing. Check your own gear, and check your partner's gear.
The armorer can unload, check, and reload the gun in front of the actor. Then the actor can unload, check, and reload the gun under the training and supervisions if the armorer. Any actor seeking to hold a real gun should also need independent, verified training that comes from outside the studio. We don't let actors fly planes or perform surgery to make the shot slightly more realistic unless they have valid training, why should guns be any different?
There is also no valid reason (cost is not a valid reason) for why there would be a real bullet that fits in a real gun (the lead projectile part) anywhere on set. Even if you need a shot with one, don't make it out of metal or anything strong enough to survive the blank going off.
Whoeve loaded the gun is partially responsible. Alec Baldwin the producer is the most responsible. And Alec Baldwin the actor is partially responsible.