Desperate Girl chooses at random one person, not knowing their role to take down with her. So she might choose the demon by pure luck, or she might take out the Gifted Girl with her.
I was just using an example saying that when the Desperate Girl is lynched, and she chooses a name to take with her, she MIGHT take out the GG when she does, not realizing it, or she might give you a break and take out the Demon. There is no way of knowing who she takes down with her until they die.
That makes the desperate girl good for the village, since anyone who counter claims must then also agree that they don't mind being lynched so they can shoot the counter-claimer.