I think we should have a general "catastrophic loss" public insurance system. Such a system would go a long way toward what Republicans call "tort reform". In many cases of medical malpractice, for instance, plaintiffs deserve recovery, but the burden should not fall on individual doctors or even the medical profession in general. Such insurance would allow people who suffer losses through no fault of their own to recover without burdening a particular sector of the economy disproportionately.
Why does it have to be public? Who pays the premiums the owner or the taxpayer?
In the insurance business there is a term called "moral hazard" which means that by insuring against some event you increase the risk that it will happen. An example would be building a home in a location where it is known that floods are likely. An insurance company would charge you a very high premium or refuse to insure such a house at all, so the owner would probably conclude that it was not practical to build a home there. But if the government guarantees insurance on the home then the owner will build it knowing that if it does get destroyed by a flood the government will pay for it. So that type of insurance promotes risky behavior.