You have a choice between public and private insurance. And you can very well be publicly insured should you desire so (for a cost). It’s just that if you don’t have an employer you pay full medical insurance premium (not half). But should you get bankrupt you will get the public medical insurance benefits for free again.
> Even if you are self-employed, you can also decide whether you wish to be insured via the statutory health insurance scheme or through a private fund.