The insurance companies have insurance to cover them in these cases.

Look up “reinsurance” or “re-insurance.” Most insurance companies back themselves with the help of other insurance companies to help diversify the risk.

then they are pretty poorly managed company – policies are usually covered by other insurance companies in that kind of situation

NO insurance company has the funds to pay 100% of all outstanding policies – it’s impossible

premiums are all based on probabilities of events happening

Here in the USA, each state has an insolvency fund, where insurance companies pay in every year, particularly to pay out in cases where something happens and an insurer doesn’t have the funds to pay the claims.

Keep in mind, it doesn’t get that far most of the time – each state is required to check the financial status of insurance companies writing insurance in that state, and usually LONG before it gets to that point, the company is put into “receivership” where the state appoints someone to wind the business down, nonrenewing policies.

Insurance companies are the most heavily regulated industry in the USA. Yes, they are required to put tens of millions of dollars aside to pay future claims, before they’re allowed to sell their first policy. The number of policies they can sell, is called their “capacity”, so they can’t oversell more coverage than they can afford to pay claims.