My daughters have them. I don't know about the running out of minutes end of things because they only ever use them when they're staying after school for drama practice and need to call to be picked up, but the ones we have (Tracfone) can be renewed every one, three, six, or twelve months with any number of minutes you want to pre-buy...I would guess, though, that if you run out of minutes, your phone would stop working, because you don't need to have a credit card to own one of these to which an over-run could be charged--you can buy the prepaid time cards anywhere like Walmart and add them on.
But yeah--I agree that just running out of batteries is probably the easiest and most "identifiable" thing to do--who hasn't forgotten to recharge their phone at some point?