'Rust' Armorer Allegedly Offered Leniency If She Could Explain Real Bullet

The armorer that's being prosecuted in the "Rust" criminal case was reportedly offered an ultimatum of sorts -- tell us how a real bullet made its way on set, or face more charges.

Variety cites emails that it says it's viewed -- which were supposedly sent to Hannah Gutierrez-Reed's legal team back in September from special prosecutor Kari Morrissey ... who's heading up the case after the D.A. recused herself.

According to the outlet -- which cites the emails that were allegedly sent -- Morrissey wrote ... "I feel very strongly she has some notion of how the live rounds came on set."

She adds, "I certainly respect her right not to come forward with that information and to stay silent, however if she were to come forward and answer some of these questions that plague the victims in this case that would go a long way toward getting her a favorable resolution."

Variety says the emails go on to float what Gutierrez-Reed's lawyers perceived as a threat ... "If she chooses not to, while I respect her decision, I will proceed with the additional felony charges we spoke of." Mind you, HGR has already said she doesn't know how a live round got into the gun that was used that day by Alec Baldwin, let alone how it got onto set.

In response to this offer, her team invoked their client's right against self-incrimination -- and lo and behold ... Gutierrez-Reed was, in fact, hit with more charges shortly thereafter.

She was accused of carrying a gun into a liquor store about 10 days after the shooting ... a 4th-degree felony. Gutierrez-Reed is already facing involuntary manslaughter charges.