Do legal moves exist in illegal position?

Do they? Or is any move in an illegal position ipso facto illegal?

The latter.

Not all illegal positions can be easily demonstrated to be illegal.

Okay...??

(this is the part where you back up your statement with an example or idea of how an illegal position wouldn't be easy to demonstrate...)

I guess you've never seen these type of puzzles. Some are ridiculously hard.

Here's a random example:

https://www.chess.com/forum/view/more-puzzles/retro-problem

This is basically how it works. You have to prove a position is legal by finding a legal series of moves reaching the position. To do that there are usually immediate difficulties to solve by backtracking from the given position (instead of working forward from the starting position).

Chess.com user Remellion has often appeared to give solution in these types of topics in the past.

@ Chin:

Ahhh...

The way the OP posed their question as a question they wanted to be answered led me to believe that it was a question they wanted to be answered, rather than an educational puzzle (like the one in your link...which makes its purpose clear from the start).

It certainly seems like the brain will get a good workout solving one of these types of puzzles, but are they a good, practical exercise for any scenarios encountered during standard chess play?  Am i missing something?  

And, back to the original question of the post:  If a position is indeed shown to be illegal, doesn't it follow that there are "ipso facto" no legal moves (because the game itself should be thrown out or restarted or backtracked to the point where things became illegal)?

Naa, they seem totally different from chess. It's its own separate kind of puzzle.

There's no correct answer. Which line of logic is correct (read as "most useful") depends on the context.

There are the points:

Later on, it continues to say about illegal moves:

So what happens if "after" a game, like, after a move producing checkmate (or stalemate, described to "end" a game in similar wording), it is found that an illegal move has been completed?

When is a checkmate illegal enough to be retracted and game resumed from last legal position?

Chess is a game that is defined by its rules. One might think of puzzles with positions impossible to reach in a Chess game as a sub-game of Chess, i.e. Chess with changes to those rules. The change the composer asks of us is that we accept the Chess-illegal position to be a valid starting point. 

It depends what you mean by "legal move". If you mean "a move made in accordance with the rules on how the pieces move", then yes. If you mean "a move which could occur in the course of a game played in accordance with the rules of chess", then no.

If the players agree on a result, then that is the final result.

So if, for example, white made some illegal moves then on the last move played checkmate, and the players shake hands and sign the scoresheets then white wins. Even if one or both players realize immediately afterwards what happened, it's too late.

However if white plays checkmate, and black stops the clocks to claim there were illegal moves, then the game wouldn't end, and the arbiter would reset the position.

@jsaepuru: Legal/illegal moves are defined in FIDE article 3.10:

1. A move is legal when all the relevant requirements of Articles 3.1 – 3.9 have  been fulfilled.
2. A move is illegal when it fails to meet the relevant requirements of Articles 3.1 – 3.9
3. A position is illegal when it cannot have been reached by any series of legal moves.

Where the whole of article 3 informs us how the pieces move. So according to this, a move is legal if the piece moved is moving as we expect, regardless of whether the initial/final positions are illegal. (See SmyslovFan's diagram.)

The articles you cited are more to do with the playing of a game. Article 5 is about defining the end of the game, article 7 more about arbitration and practical play. The question you're now asking about illegalities discovered after completion of a game is more about an arbitration issue (cf some chess game where one side castled twice); I'm inclined to say that if the mating move is legal, the game has terminated and no retraction is done.

Defining exactly what legal moves are is no easy task, especially with respect to chess problems and the subtle article 5.2b. Without traipsing into problemist territory, let's just say even grandmasters have played moves after the game ended (in accordance with 5.2b) - see this interesting page by François Labelle.

@human-in-training: No, solving retros will probably make your actual play worse. It's got almost nothing to do with practical games of chess. And yes, even just proving a position is (il)legal can be terribly complicated.

But checkmate, if legal, is supposed to end the game "immediately". It is at least customary to not press clocks after a checkmate has been "completed", by releasing the moved piece/s and removing the captured/promoted one/s

So suppose that after white has released a piece creating a checkmate position - but before signing the scoresheets, black argues that illegal move/s have been made.

White concedes that illegal moves have indeed been made - but argues that the last, checkmating move itself was not an illegal one and therefore the checkmate should stand.

What should happen?

Also: I understand that article 5.2b does not actually change the outcome of a game - it treats a position where draw is the only legal outcome of any legal moves.

Whereas article 7.5b:

"for the second completed illegal move by the same player the arbiter shall declare the game lost by this player."

Does two refer to the count of occasions, during the same game, that a player is found to have completed an illegal move, or does it refer to the count of illegal moves found?

If, when examining a problem while a game has not ended, it is found that both players have completed two or more illegal moves, what is the outcome of the game? Win for the second player to complete his second illegal move? Or both lose?

I think that it's correct to STOP the clocks once you mate the opponent, though.

I vaguely recall reading about something like that happening. In a time scramble, an illegal move was made, but the other guy moved instantly so didn't notice, then next move was mate... the checkmate was a legal move, but the one setting it up wasn't. The player who was checkmated complained, but I believe that was ruled a win for the player who gave checkmate.

I think it's always illegal in FIDE rules.  In USCF -which should be the same but are slightly different- I have been a Tournament Director and there are situations where an illegal position is allowed to stand.  The main reason, I think, is to keep tournament round times on schedule: going back a lot of moves and adding time to clocks can throw off a whole tournament.

USCF Rule 11B: Illegal Move Prior to Last Ten Moves. If it is found that an illegal move was made prior to each player's last 10 moves, the illegal move shall stand and the game shall continue.

Note that the rule means the last 10 or more moves have all been legal moves, made since the LAST illegal move. For example, if the players keep playing while a King remains in check, every move they made while the King stayed in check is illegal and they'd have to make 10 legal moves after the last move where the King was allowed to stay in check.

Why? Is there anything illegal about the position? The same position could have been reached by a legal series of moves - one where the king did not forfeit the castling rights. Or one where artificial castling was performed.

In rabid chess, the rule is A.4b:

"If the opponent does not claim and the arbiter does not intervene, the illegal move shall stand and the game shall continue. Once the opponent has made his next move, an illegal move cannot be corrected unless this is agreed by the players without intervention of the arbiter."

That does not apply in slow chess. Meaning that an illegal move which goes unnoticed at first must be retracted if noticed until... when? Up to the time both scoresheets are signed, or up to the time a checkmating (or stalemating) move has been made?