There's Still Hope For These Dead Game of Thrones Characters — in the Books

How he dies on the show: After battling Roose Bolton's army at Winterfell, Brienne of Tarth comes upon Stannis resting beneath a tree and kills him to avenge his brother Renly's death.

Where he's last seen in the books: In A Dance With Dragons, Jon receives a letter from Ramsay Bolton claiming that Stannis has died in battle at Winterfell (the same battle as what we see on the show), but his death is not confirmed, and Jon doubts the veracity of the letter.