Proper procedure is for the prop master and armorer to be responsible for making sure the weapon is safe. They will then hand it off to whoever, and will loudly announce "cold gun".
The gun can be handed to an assistant or the actor, if it is passed to an assistant first, when they hand it over to the actor they, too, must announce "cold gun".
This lets everyone on set know that the gun has been verified safe by the armorer.
Baldwin was handed a gun, and the person handing it over loudly announced "cold gun". He was then expected to treat it like it was not loaded, because he was loudly told.
The reason why you hire an armorer in the first place is because you don't want your actors to think they know how to handle weapons. You want positive control of every weapon on set.
That broke down on the Rust set.
The story of how that broke down on the Rust set is actually quite interesting. It was a combination of nepotism (the armorer was the daughter of a famous armorer, and got the job through her dad's connections) and the complete failure on the part of a prop company.
See, the live rounds were reloads, loaded into the exact same casings as the dummy rounds normally used. The reason the reloads were made was actually valid. A different armorer on a different film shoot made them to let the actors of that film get an idea of how the guns they were using would actually kick.
At the end of that film, the live rounds got co-mingled with the returned dummy rounds, and then those co-mingled rounds were rented out to the Rust production.
The armorer for Rust should have caught these rounds. They were not completely identical to the dummy rounds. But this was her second film, and she had never actually worked with live ammo.
When questioned by police after the shooting, she didn't even know the brand name on the dummy rounds.
Anyway, she had prepped the gun for filming, and then the assistant director took it from her cart and handed it to Baldwin, announcing "cold gun". The assistant director did not check the gun either, he just grabbed it and handed it off.
As a note, there were not supposed to be any live rounds, or even any blanks on set. Just dummy rounds.
The other failure here was actually sort of on the victims. Industry standards for filming scenes like that is to use a monitor, and not have anyone standing in the potential path of a bullet, even if there are no bullets. The cinematographer and director were both standing behind the camera. Mostly because setting up a monitor takes time, and they were under a bit of a crunch to get the scene filmed.