Here's what happens:
* Elena breaks up with Stefan. She chooses to be with Damon, believing that she can't be with Stefan without him being tortured by his humanity.
* Stefan turns off his humanity. In an act of self-preservation, he decides he can't keep living with the pain of losing Elena, so he chooses to be emotionless.
Therefore, at the end of Season 2, Stefan and Elena are not a couple. They are broken up, and Stefan has actively chosen to shut off his emotions, making any chance of them getting back together in the near future seem extremely unlikely.