Thinking about how in Hebrew a very common slang term for loving something is "I'm dead (or dying) on". So saying to someone "I'm dying on you" is a way of showing affection and closeness.
Also a way people (usually women, but not exclusively) sometimes refer to people they're close to or like is to call them a "soul" or "my soul".
So you might hear someone saying "dying on you, my soul" extremely casually.
edit: just remembered sometimes people use "my life" instead of "my soul", leading to the even more confusing sentence "dying on you, my life"