First of all, I'm going with PAX on a few things. As stated, the BG is attempting to move you from a situation where they DO NOT have optimum control. Therefore, YOU DO NOT LEAVE. If you die in this attempt, you have still foiled the BG. All bets are off if you allow yourself to totally lose control.
Mr. Brit is correct. Shots to the brain stem WILL drop a person...PERIOD. The shot HAS to be thru the brain stem, however. Shooting them between the eyes, simply means a round went between the two main cerebral cortices, and may or may not have nicked the cerebellum. Nothing guaranteed there.
I've been unfortunate enough to have to deal with something akin to this. I've been blessed enough to come up on the winning side. Yes, there is a winning side to this situation. You're alive, loved one is alive, BG is crapping their shorts autonomically as they bleed out a ragged hole in the base of their skull.
No, I do NOT want to try it again. Enough nightmares there for one lifetime...