It's not the dystopia its made out to be but even in the best states the inconsistencies between the layers of protection and myriad of rules cause a lot of people to fall through the cracks.
Also, if you work a service job and miss too many shifts due to illness, they'll just fire you for being unreliable.
* 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.
Looking back, all of me previous jobs have offered 10 days sick pay and I've always assumed it is a de-facto standard over here.