I hadn't known that was possible, either, until last month when I came across an extraordinary position in the book "Basic Endgame Strategy: Kings, Pawns, & Minor Pieces" (Bill Robertie, 1998, New York, NY: Cardoza Publishing). In one puzzle, White has a hopelessly lost endgame yet he could still draw by walking his king into his own box-like cluster of pawns that couldn't advance due to Black's opposing pawns, then by closing the door behind him by advancing a pawn behind him. Even though Black queens a pawn immediately before White "closes the door," it would take one move for Black to move his new queen over to that box, then another move to sacrifice that queen by capturing a pawn of that box, just so White can't die by self-suffocation! That was an extraordinary save I would never have noticed in a game unless I already knew it were possible. (By the way, if you look up that book, there's a typo in the diagram: White's h pawn is missing from the diagram. Fortunately the copy of the book I saw was a library book where somebody had drawn in the missing pawn.)
P.S.--Can you post your game? I would like to see it, and I think other people would, too.
Strange game today, I was checked so moved my king into a stalemate position! I had only my king remaining, my opponent was unable to check or checkmate me or move a piece that would permit me to move. I did not know this was possible.
Regs,
Tim