9mm. Hmmm. Probably, then, a semi-auto. I've seen a 70-Series Colt GM dropped, cocked but not locked, on its slide, and it did not discharge. I saw another drop-kicked after the shooter made the common mistake of trying to grab it after it slipped from his grasp; no discharge. I saw a guy trip after being startled, land on his face and inadvertently fling his Hi-Power, cocked but not locked, across the floor and against a wall, without it discharging. The armorer of a former employer would torture Sigs, hammer cocked, and experienced no discharges.
The only AD I witnessed where the shooter did not have his finger on the trigger, was a Colt GM Series-70 that first suffered a FTFire followed by a FTExtract. The cartridge apparently jammed in the chamber and the slide jammed slightly out of battery. The shooter forced the slide backward and it slipped from his grasp. The breach face hit the out-of-battery primer, the firing pin then detonating it. The bullet exited the barrel, plopping on the floor about two meters away. Noisy, frightening, but nobody hurt. We then took him outside and beat him to death. Just kidding . . .. But we WANTED to.
Our youngest son is a LEO, and took to Glocks like a fish to water and has been issued them by the departments, as well as buying his own. He has not tried to make one fire by dropping it (which he would have done with it unloaded), but he says it isn't possible if the trigger is not held back.
Another son is professional military and relates disgraceful gun handling he witnessed in the desert, where M9 Berettas fell out of holsters onto hard surfaces without discharging.
I don't remember for sure, but I believe that all the guns submitted for US military consideration to replace the M1911 were dropped on the muzzle from four feet, and flung across a concrete floor to bounce off a concrete wall, some distance of six (or more?) feet. I recall some early failures, but all final submissions met that standard.
Just as I believe most "cleaning" accidents were actually the result of "practicing" quick draw with a loaded gun, I wonder if the lady had her finger on the trigger as she moved it, perhaps "practicing" with it behind the closed door. To me, a modern semi-auto in good condition firing solely from being dropped is unlikely. I feel confident that I could pound any of my semi-autos on the muzzle, hammer, or anywhere else and they would not discharge.
Regardless, I feel as several others who posted, that something happened that could not be ignored. I doubt anyone involved could have defended keeping her employed, there.