Well, they don't really "live" but they exist as an entitysorta. But everything does. :\ Wouldn't be as much fun if all our molecules had seperate souls and stuff.
I've always considered it more a question of interaction rather than simply 'being', a star
does interact with it's surroundings, it responds to outside influences and influences things outside itself.
That said it has no 'consciousness' as such, which makes matters unlikely, it's not aware of the Universe around it, which has always struck me as a quintessential definition of higher life-forms. Bacteria, for example responds more to stimuli that through any coherent thought, so the odds, to my mind, of Bacteria having anything that could be defined as a 'soul' are pretty slim to none.