here someone with "freiwillige versicherung". There are 3 issuance types:
* Obligatory (public), when incomes < 5.000 / month
* Voluntary (public), when incomes > 5.000 / month, but you decide to stay on the "public system"
* Private, when incomes > 5.000 / month
When voluntary, you are supposed to pay your contributions directly to your KK. Anyway, if your company is nice, they can do it for you.
Regarding KA, I think it is not an issue. You know, 60% from difference between regular nett and reduction. However, your employer has to continue paying their contributions (except AV). The tax basis is reduced on 80% from difference between regular and reduction. So, if reduction is 100%, the company shouldn't pay any contribution, as they are not paying you (sounds logic, right?). Anyway, you are not supposed to pay twice. This link explains it better than me (in German):
Let's think, your KA is calculated from your nett (i.e. after taxes, RV, KV, ..., etc.), and then you have to pay KV+PV again? Then, why not paying RV as well? A bit more and you have to pay to the Government xD If you had to pay your contributions, it would be fair to calculate the KA before SVs (IMHO). Don't you? If not, it is a trap.
Please let us know about your case