You don't lose any karma for letting him kill her. Come to think, you don't lose Karma that much in this game when completing quests. In your case, it's based off of your personal preference, morals, doctrines, etc. Do you want a [censored]-ton of caps? Do you care about her enough to save her life? In my opinion I think she's suicidal from the way she acts. She's lost her Caravans, she has nothing to live for. No father or mother, just whiskey. I think she's better off in a better place, and you're better off with thousands of caps.