> I find the whole notion of "sick days" and accruing them bizarre.
Agreed. Companies here in the US are pretty stingy with them, too, causing people to come to work sick where they get everyone else sick too.
> What happens if you're sick but don't have enough sick days saved? Are you fired? Stop getting payed?
You stop getting paid and can be fired if the company wishes.
Some companies are subject to FMLA, which protects your job for 12 weeks of unpaid sick leave. Its requirements rule out small businesses and new employees, though:
> In order to be eligible for FMLA leave, an employee must have been at the business at least 12 months, and worked at least 1,250 hours over the past 12 months, and work at a location where the company employs 50 or more employees within 75 miles.