White's time runs out in this position. What's the result according to FIDE rules?

True. The move creating the position has to be legal 

But I feel that in the original post, even if White plays an illegal move, Black cannot be declared won, since the fact that Black cannot escape the otherwise forced legal mating sequence remains unchanged. This is similar in principle to the running out of time scenario.

Yeah, I was referring to later posts.

#9 The arbiter is totally right, just because it is not checkmate yet! (Big thanks to a5 bishop, otherwise I wouldn't know what to say).

P. S. Also, White can win by promoting a pawn.

(still writing about #9) Wait, I just realized that until the piece is dropped, the move is considered not made. So even if it was checkmate White would still win on time, (I know this is a MASSIVE epic fail for Black)

It is quite a pity that Black was just one moment too late.

I am rather curious. In the original post, if White has time left, but instead chooses to resign (for some awkward reason or another), will Black be considered to have won because White resigned, or will the outcome be a draw due to the impossibility of checkmate by Black?

Resignation ends the game.

There have been plenty of examples of players resigning drawn or even won games.

The player whose opponent resigns always wins the game; check FIDE Laws of Chess. (I also thought that it might be a draw if the opponent can't checkmate, but turns out that nope, the opponent wins.)

IF I was still a USCF Tournament Director, I would rule it a draw.

Someone commented that it would be a draw FIDE and Black win USCF,

I can't speak for FIDE, but USCF Rule 14D4 says it's a draw if there are "No legal moves leading to checkmate by opponent." Rule 14E shows that applies "even when a player exceeds the time limit."

White's forced move would have been 1 N(either one)xg6+.  From that position Black does not have a REASONABLE chance to win as 1...Qxg6+ is forced as is 2 Nxg6#.

This position would be a draw. The moves 1. any knight takes g6 and then queen takes g6 ARE FORCED BECAUSE OTHERWISE IT IS MATE. then the move 2. other knight takes g6 IS MATE so that makes it a draw because white's flag fell.

So the only way for Black to win the game is when White resigns on the spot.

Plenty of people have mentioned this position would yield a draw. I agree as far as the rules are concerned. However a position like this arising would be reason to reconsider the rules for future events. Even though this is a constructed position one could argue that, even when out of time, if every legal continuation leads to mate for him its a win. At least that is the sensible thing to do.

THE famous example for this is the Timman Velimirovic ending with Timman as white. With pawns on a2 (White) and a3 (Black) Timman a rook and Velimirovic a bishop covering a3, this game was crucial for the 1981 interzonal result deciding on the candidates for the world championship. Cheron gave 60 moves to decide the game but Timman improved on that and won within 50 moves thus qualifying. Because of this endgame the 50 move rule has been adapted allowing 75 for this endgame.

The point being that rules are not meant to defy the nature of the game which in this topics example clearly is the case.

As for the rule book there is a funny case that I unfortunately don't have handy. Its a retrograde problem with all material on the board where you can deduce there are 50 moves needed to get to the shown position. The point of the problem is that you can claim a draw since the French rules of FIDE state the 50 move rule as "No pawn moves OR pieces captured within 50 moves". OR should be AND no...

Just saying

White didn't manage the time well, so White doesn't deserve the win. Black didn't manage the board well, so Black doesn't deserve the win. In my opinion a draw is the intuitively correct result.

Yes, some retro problems involve the 50-move rule to force the result is a draw. (Some problems go further than that; the stipulation for retro problems is that 50-move rule is an automatic draw, so if we look back more than 50 moves behind, some player might be forced to make a suboptimal pawn move or unit capture to avoid triggering the 50-move rule. I remember seeing a "retract 2400 moves and mate in 1" problem. It's weird.)

And yes, it should be read as "no pawn move and no unit captured in the past 50 moves". Or by De Morgan's law, "neither pawn move nor unit captured happened in the past 50 moves".

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If anyone saw the post before I deleted it, I had the Bishops in the wrong position.  Made a world of difference.

Going off topic from the forum title, seems like this also means that if I resign when I have a king and a queen and the opponent only has a bare king, with the position not being in checkmate or stalemate, my opponent would have won by my resignation.

Yup, Eric. The only time that resignation doesn't end the game is when there's checkmate or stalemate on the board. It's hard to imagine playing checkmate, then resigning though.