The dunmer necromancer refuses to leave the cave. Ive tried spells,arrows and shouts anything work that forces her to leave. If she dies the quest does not change and stays in log

She is so logical that she refuses to leave the cave if there is any danger inside it. That can include the fox!

Is this the one in the cave somewhere in the mountains south-ish of Helgen?

I had to "force" her out with Unrelenting Force.