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.

This is not true.

> 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.

http://www.bamf.de/EN/Willkommen/BankenVersicherungen/Sozial...

Self-employed you can be in a public health insurance. Depending on income you might switch to private though.

More relevant: self-employed don't pay into social security. Thus unemployment money and retirement have to be paid differently.