n0mesora
“My point is, since brain death will never be declared on a breathing patient, (Because if they can breath on their own that proves a functioning brain.) the question became inapplicable.”
Again I’m not sure what you mean. Your first sentence is correct. but not the seocnd People are declared dead via brain dead standard daily. It is not at all inapplicable. As part of the determination, the vent which is ventilating the non-breathing patient s shut off (after pre-oxygenating the patient) and they wait a bit to see if the patient breathes. If he does he is not declared dead. If he doesn’t breathe he is dead. At thsi point the vent is reconnected to potentially allow for organ donation
“That because of brain trauma one can be declared dead even though there is a possibility of the lungs still working on their own”
The lungs don’t “work on their own” each and every breath is directly controlled by the brain (technically brain stem). In the absence of a brain the patient doesnt breathe. Again, NOT becasue there is anything wrong with his lungs (this may have been what you meant) his lungs are perfectly fine (in fact these lungs can potentially be used for someone else by transplanting them). But he is not breathing because the brain isnt “telling” him to.
As a reminder the heart may still be beating, since unlike the lungs, the heart is not controlled by the brain.
So the question becomes what is the halachic status of a person with no brain function, who cannot breathe on his own, but whose heart is still beating .
Most poskim say since his heart is beating he is alive period.
R’ Moshe seems to say in his teshuvas (and his son R’ Dovid explicitly said he held this way) says this patient is not alive because he isnt breathing. R’ Ovadiah Yosef held this way as well
(other poskim held he is dead because it is considered as if he is decapitated which mishna in Ohelos says is dead but whtehr this accurately describes a brain dead patient is questionable)