Nope. It definitely can't happen in the game of chess. You might try playing a variant where the rules are different, but there isn't anything like this in chess.
Question about obscure chess rule - King takes own pawn to escape check

I do not know if official chess rules state that a player cannot capture his/her own men, but I think I read somewhere that you can't. However, did you know that in England a Knight is depicted by a horse and rider, with the rider holding a shield? The shield prevents the Knight from being captured as long as it has the opposing King in check!
I'm playing a game with a friend, and we're trying to figure out if there's a rule that allows one to capture his own Pawn to escape from Check...
Anyone heard of this rule?