In brain death, the entire brain including the brain stem is dead. You shut off the machine and they quickly die because the lower part of the brain stem that controls breathing and the heart don't work.
In acute head trauma, or in major intercranial hemorrhage from strokes, often the brain swells on day 2 to 5, shutting off all circulation to the brain, so the brain dies...and yes they are indeed dead: Only the machines are there keeping the body alive. I believe this is what is happening here.
But it is morally acceptable to remove the respirator even if the person is not brain dead.
Finally, the Catholic church does not mandate keeping someone on a respirator, because it is acceptable to refuse extraordinary treatment.
We had a relative here in the Philippines on a respirator after a massive stroke for a week. He was not brain dead...But he was 80 years old, and it was obvious he would never wake up, so we had the respirator removed and the family stayed with him until he died the next day, not of euthanasia but of his stroke.
Until recent times, this definition included feeding tubes as optional, but Pope John Paul II recognized that these tubes, which are not painful and do not require expert nursing, were being removed with objective to kill the patient. That is what happened with Schiavo, whose husband was ready to remarry and she was in the way and depleting the family's money in a nursing home.
But I had a patient who could not swallow and refused the feeding tube, mainly because when he was tube fed they kept him isolated in his room and he wanted to go outside his room and recreate at lunch. Alas, he died a few days later of aspiration pneumonia. And the legal case that said this was okay was the Brophy case, a fireman who swore he never wanted to be kept alive on machines. He was comatose from a stroke, and the wife, with the church's approval, had the tube removed.
Now, one word of caution: there is a move in medical ethics to broaden the criteria of brain death from whole brain death to something called higher brain death. There is also a trend to take organs from people who are dying but not brain dead: They let the heart stop, then remove the organs. And there have been cases where brain death was misdiagnosed and woke up, but these cases are rare. these decisions are subtle. Get a good pro life doctor to help you judge such cases.
That would make sense. I linked a video in the post just above yours where Anne sat up on the gurney as she was being hauled to the ambulance. She sat up, looked around, leaned forward, and reached for either the sheet she was covered with or those pushing the gurney. That wouldn't be brain death, but swelling a day or two later makes more sense of the video.
I had a family member who’s upper brain functions were gone due to a stroke, but the hospital staff “weaned” them off the machines that were keeping them alive.
As a result, even though this person had absolutely NO response to stimulus (no response to removing the tracheal intubation, no response to sharp poking, nothing), the body lived on for roughly 10 days.
This person was given an IV drip of nutrients and hydration, but that’s it. We had to fight for that - the hospital didn’t want to give them ANYTHING - and this was AFTER they “weened” them off the machines keeping them alive.
In my opinion, this “weening” denied this family member a faster, more humane, natural death.
I was right in the middle of all this, and it wasn’t fun at all. It showed me first-hand how in the modern medical system, death can be more of a drawn-out process than an event.