If a batsman stands his ground and no appeal is made by the fielding side then he should not be given out by an umpire, even if he should be out under the Laws of the game.

BBC: Umpires

If a batsman stands their ground and no appeal is made by the fielding side, then they shouldn't be given out by an umpire.

BBC: Sport Academy | Cricket | Rules | The basics | Umpires