In pool, what happens if the last coloured ball and the white are sunk in the same shot?

Officially, the game is not over if the 8-ball is not sunk, and the opposition player gets to shoot next. However, this varies significantly between regions, and in many locations the game will end. See link:

If the player knocks the 8 ball off the table then the player loses the game. If the player pockets the 8 ball and commits a foul or pockets it into another pocket than the one designated then the player loses the game

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Otherwise (i.e., if the 8 ball is neither pocketed nor knocked off the table) the shooter's turn is simply over, even if a foul occurs. In short, a World Standardized Rules game of eight-ball, like a game of nine-ball, is not over until the "money ball" is no longer on the table.