Though Salazar wants everyone to be a pure blood in his house, things change when he leaves because he now can't handpick his students. As with every other family, there are oddities within so it is not likely that ALL of Slytherin's posterity goes to Hogwarts or that they all go to the Slytherin House. Snape was the head of Slytherin house and he is a half blood, hence the name of the 6th book/film; Harry Potter and the Half-Blood Prince.