The first month after getting unemployed is free, after that either the unemployment insurance or the government takes over your payment.

If you have to pay the fee on your own and miss at least two months (which can't really happen for regular employees as the fee is taken directly out of their paycheck) the fees can be collected with exactly the same procedure as other taxes. Until this happens you are only covered in an acute illness or pain situation, pregnancy, and for some preventive checkups. Health insurance (both private and public) can never be cancelled for nonpayment.