Her brain stem is dead along with the rest of her brain. Yes her heart continues to beat with the aid of a ventilator pumping oxygen into her lungs. But it won't keep doing this forever. Her blood pressure is already very low and continues to drop. Read the link to the article I posted above. It explains things a lot better than I can.
Um, your lack of education is showing. If the brain stem is dead, the heart is not beating without external stimulation.