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The additional move for the lone King will still be required for this preset, but the Bare King rule precedence over Stalemate will assign the win to the correct player.
I would expect the White player in the center position to resign, rather than to play, but if he plays the preset logic will now award the win to Black (no matter what White plays), and formally end the game.

Note that, despite the clever construction of the position, this is basically a non-issue: irrespective of the rule precedence the given position is always a win for black, as he can also bare by Kxa2.
Hi H.G.
I thought about trying to find a position with a stalemate by bared K created by a series of forced moves (such as in a problem), but it seemed unnecessary at the time, as even though the 'stalemate' can be prevented in the initial position I gave, there's still the possibility of the 'error' I selected as the only line of play, which at least shows that such a final 'stalemate' could possibly arise by legal moves in a real game (and I've seen some pretty bad legal moves played over the years...).
Question for H.G. (or any who might know):
Are two opposite-coloured FA (ferfil) elephants on average worth more than one FA plus N (or worth more than 2 Ns) on 8x8, according to computer studies?
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I fixed the preset. Now it will correctly give preference to a win by Bare King over Stalemate, and will correctly give the win to Player B in the position that Kevin had sugested below.