Yes, Max is brain dead in Stranger Things. When speaking with Josh Horowitz on his podcast, the Duffer Brothers said that although Max is alive, she is "brain dead, blind, and all of her bones are broken."
OK, we are confused because, according to the NHS, a person who is brain dead is "legally confirmed as dead" and has "no chance of recovery because their body is unable to survive without artificial life support."
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So, what is the truth? It's possible the Duffers are misdirecting fans. In the episode titled "Papa," Dr. Martin Brenner (Matthew Modine) reveals that Vecna "takes everything from his victims ... their memories, their abilities," indicating that the antagonist absorbs everything from his victims, inside and out.
Therefore, this is likely what happens to Max and is why El can't find her in the Void; even though Max is still technically alive, there's nothing left of her except her physical body. Hopefully, El manages to save Max before it's too late.
All four seasons of Stranger Things are currently streaming on Netflix.