If Joker's wife didn't die, it would significantly change his backstory and motivations for becoming a criminal mastermind. However, it is important to remember that the backstory of Joker varies depending on the comic book, movie, or TV show adaptation. In some adaptions, Joker's wife or girlfriend is portrayed as a tragic figure who is killed as a result of his actions, while in others, she does not exist at all. So, if you could provide more context or specify which adaptation you are referring to, I could assist you better.