In competition blitz games, making an illegal move and then pressing the clock forfeits the game if the opponent claims the illegal move as long as they do not make a new move, as a new move would void the previous illegal move according to FIDE blitz rules.
I've seen all kind of forfeits because of this reason in blitz games, including one player taking one of his own pawns.
However, the most common case for illegal moves is neglecting that the King is in check or unprotecting the King. In this case where the King is checked, if the opponent takes the exposed king and presses the clock, are they making a new illegal move, hence voiding the previous one?
I've been told that taking the King, even as a kind of "joke" to expose a previous illegal move, is an illegal move by itself, because the King cannot be taken, only mated. Is this true under FIDE rules?