That’s not correct. Your employer has to continue paying you for up to six weeks. (You generally need a doctor’s note after three days.) If you are sick longer than that your health insurance has to pay you some of your wage, usually 70 percent of your gross wage and at most 90 percent of your net wage.
Yes, you are correct. Last time I was sick for a few days I had to bring in the doctors note, which was handed over to the bookkeeper. I assumed, wrongly, they turned it into the state to recover costs. Which is what happens when I buy things for work, travel for work, or use a hotel for work.
But I think the 80/20 split is still in effect for anything longer than a few weeks.