The Federal Office of Public Health oversees not only the mandatory basic insurance offered by the individual health insurance companies but also their reserves: inspection results of 2012 (this PDF document also contains some explanatory notes in German).
This constitutes a first safety level to make sure that outstanding benefits can be paid out to the policyholders. Moreover, thanks to reinsurance for costly cases and participation in a security fund, you have guaranteed financial security even with smaller providers. The Health Insurance Act obliges all insurers to participate in such a fund. Should a provider happen to be unable to pay the benefits, this security fund would cover the costs.
An appropriate balance of policyholder profiles (percentage of men, women and children; low average age) is decisive for low premiums. According to RVK, smaller and medium-sized providers have a good balance of profiles and a correspondingly low risk, which is why they have to pay contributions to health insurers with less favourable profiles.