In a fight, she’s going to die. The only way to get past his sword is to kill him preemptively. Once the sword is out, she’s dead. More than that, she has no way to close the distance to even injure him. Quite literally, she will not even slow him down. This isn’t a background question, or a gender question, it’s just a weapons issue.
He’s swinging a 5 – 6 foot long blade that weighs about as much as your laptop (4 – 7 lbs). We can talk about it being slow (for a sword) or heavy (for a sword) but it’s very important to understand, she cannot get within six feet of him and live. It’s still a very agile, lethal, and fast weapon.
It’s also important to remember he’s not a video game character. He’s not going to make some big overly telegraphed attack and then end up with the sword buried in the masonry long enough for her to run up and shank him a couple times. Doesn’t happen.
If she never fights him. She just comes up behind him in a crowd, buries her dagger in his kidneys, and leaves him to bleed to death, she can come out on top. But a quick assassination strike is her only option. Really, that’s the combat role of a dagger, outside of some very situational stuff.
So you have a character that’s geared for heavy infantry combat vs. a character who is effectively unarmed. That’s never a good situation.
Also? She should know that. When you’re talking about someone who’s effectively an opportunist, she would know she has no chance in a stand up fight with a soldier/ex-soldier/merc. If presented with this guy, her options are to either shank him, or run. If he’s ready for a fight, then she needs to be someplace else, now. Someplace he can’t follow her. If that’s through a black market he can’t enter, through a church, into somewhere neither of them want to be (like the tavern they’ve both been thrown out of for completely different reasons) but that will raise less of a fuss over an “unarmed” woman racing in, than a main armed with a greatsword. Because, honestly, a big guy with a greatsword barreling into anywhere is rarely a welcome sight.
It’s important to understand, running isn’t cowardice. A character choosing not to commit suicide against an armed opponent in a back alley brawl is just being smart.
On a writing level, I’m going to leave you with a question: If it doesn’t matter for the plot, then why is it there at all?
Whenever you’re working on a scene, it needs to be in the story for a reason. It needs to move the plot forward, or provide more character development. Something. It needs to do something.
Killing off a character because, “eh, might as well,” is usually a bad idea. There are legitimate reasons to do so, but they get into some really tricky territory. Killing characters to promote the idea that, “no one is safe,” can easily backfire, leaving you with readers that no longer care. Even in the best circumstances, the more characters you kill, the less their deaths matter.
Simply snuffing peripheral characters because you can, doesn’t really get you anything. If neither of these characters are important enough to affect the course of the plot, why are you spending time looking at them fighting? It becomes a weird kind of filler that can just as easily be cut.