Nope, everything stays. including you're profile with you're questions and answers. Also when you quit, it'd be impossible for them to re open it back up (either that or they don't want to allow it). so its pretty pointless deleting it... if you keep it but just stop using it... at least you have some degree of right over you're profile. When you quit you will still be here
Answers/questions are not erased, just hard to gain access to if your profile is set to private. But if you should delete an account, you have zero access to the messages you have sent/received. That information is lost.