I always thought "brain dead" meant no brain function, and they only continued the respirator and heart pump long enough to "harvest" the organs (where that is a consideration).
Yup. THAT is the condition under which the RC Church allows withdrawal of life support machinery (not the same as nutrition/hydration.)
There is no brain function which triggers breathing, heart activity, etc.---that's brain-dead.
Now there's a whole long discussion of under exactly what circumstances 'organ donations/transfers' are acceptable...
That is what it means. JimmyClyde the Greatest Neurologist in the Known Universe has decided it means the same thing as "minimally conscious."