However, there is a subcategory of twists that happen much earlier in the movie, in and around the half-way mark, that sends the rest of the plot in an unexpected direction.
Be it the sudden killing-off of what initially seemed to be our primary characters in the likes of Psycho or Death Proof, or a sudden jump in genre, like action to horror in Predator, or crime thriller to horror in From Dusk Til Dawn, also usually accompanied by the sudden death of a major character.
However, movies like those, you're almost ready for that kind of surprise, because either (A) it was heavily implied in the marketing, or (B) you're watching a movie that automatically lends itself to big shocks.