Rebirth and brain death
The common stock phrase the Buddha used to describe rebirth process in many suttas:


  "...because of performing and undertaking such action, on the dissolution of the body, after death, s/he reappears in a happy/unhappy destination..


A brain-dead person is not dead yet. When the body is officially dead, there'd be the full departure of 3 things: vitality, body heat, and consciousness (MN 43).
So, does this person gets reborn? No, since s/he's not dead yet. What if medicine brings him back to life? That'd be great. What if this person would be left in this condition forever by keeping that person alive with medical resources? S/he is still who s/he is, but just like taking a long deep sleep..