There's a few possibilities I can think of:
* Unpaid sick days
* The limitation is the other way around, they don't want to give a single pool of 30 paid days off, you're limited to 15 vacation days
* If you have a good relationship with your manager, it's a soft limit and they'll allow you to go over as long as it's not abused
* If you're part-time/hourly, trading days/hours with a co-worker
Our HR department combined vacation days and sick days into one pool several years ago when they realized most of us were faking sick days to get more vacation time.