[skwb]

Most insurance works on the basis that we have some underlying risk (probability) and resulting cost (multiplied together gives us the expectation) of annual payout. A lot of these funds however are financed through CAT bonds [1]. The idea of CAT bonds is that the sort of financial business cycle (a la 2007/8 housing market crash) are decorrelated enough with other financial movements that you "shouldn't™" both have a bad natural disaster and a sudden shift in the business cycle. However, a lot of these insurance companies are then further reinsured with specific contractual limitations so that ideally the fund won't run out.

In the real world, the government can act as insurer of last resort and use tax dollars to with financing (though these usually are ideally set up with the initial fund).

[1]. https://www.investopedia.com/terms/c/catastrophebond.asp