The liability is capped at a certain amount. In the US, that is around $450 million per reactor. They also have to buy in to a fond. In France, the cap is 700 million euro. Above that, the federal government _could_ step in. The problem is, no private insurer (or even pool of insurers) could cover the absolute worst-case GAU, and not even the government really.

In Fukushima, TEPCO was required pay $1.5 billion. But the real cost is / was around $150 billion. So, the bulk of the disaster was not covered / covered by the taxpayer. So: the public.