I would just like to know if her heart will beat, unassisted, so long as oxygen is pumped into her lungs. If so, she is circulating her own blood thus her brain --right down to the stem-- is not yet 'dead'. She is not yet a cadaver if her heart will beat on its own so long as 02 level is maintained by machinery if needed.
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.