But in some sort of abeyance?

body begins to deteriorate?

During the dying process there is some sort of chemical change in the brain.

Chemicals blocking the cognitive processes are dying too.
Or some chemicals are produced which enhance brain functioning.

If researchers could study this in more depth, maybe we could find a cure
for dementia?

I used to watch 60 Minutes every week when my dad was in a nursing home with Parkinson's-related dementia. It was his favorite program. He was pretty much nonverbal by this point in his life. He had worked most of his career in the oil industry.

The program did a segment on the merger of Exxon and Mobil. He suddenly blurted out "Too much concentrated power". That was the last coherent thing I remember him saying.

I've never seen this rally linked specifically to dementia patients; it's been observed in terminal patients in general. A brief spurt of energy and lucidity can fool family into thinking their loved one is recovering (despite medical staff telling them differently); the ensuing death catches them by surprise (and may lead to them blaming the medical staff).

My own mother experienced this bounce. Over the course of months she had been increasingly confused by a series of mini-strokes, then one afternoon she was perfectly composed, lucid, even cheerful. We chatted about her finishing her memoirs (at this point she couldn't read or write) and made plans to go on an outing. A few days later she crashed -- weak, cold to the touch as her circulation shut down -- and she slipped into coma while at the ER. She died a few hours later.