A rabbi tells me: “I have not read the RCA’s position paper, but I have read hundreds of medical textbooks and journals. I have been present many times when doctors were doing a brain stem death protocol and it is clear that the person is dead. When the gemara (last perek in Yoma) says that both heart and lung function are how we know if someone is alive or dead, it is talking about examining a person under a collapsed building or wall, this is spontaneous breathing and heart function. To extent that to the case where only mechanically is the body kept alive organically seems to be quite a stretch. I think Rabbi Moshe Tendler‘s position is correct. This has also been the position of the rabbis Shlomo Goren, Ovadia Yosef, Mordechai Eliyahu, Avraham Shapira. Many times when Rav Shlomo Zalman Auerbach was confronted with this question, (he was one of those that rejected brain stem death) he would always send the question to Rav Avraham Shapira (in order to save a life).”
I understand that the brain stem is the last part of the brain to cease functioning. This continues after all cognitive abilities are gone.
Heart, liver and lung transplants are unique. Those organs have to be harvested while the heart is still pumping blood. If you wait three seconds after the heart has stopped pumping blood, they will deteriorate so they will not work in another body.