Most self insure, but have a catastrophe insurance. (I forget it’s official name), but effectively it is an Insurance with a very high excess, something like £10m. Details are usually available by looking at the companies Accounts on Companies House website, and looking in the notes under liabilites or contingencies.
Therefore only covered for huge claim events, which would have severe impact on cashflow.
These types of Insurance will have a lead insurer, and percentages will be reinsured with others so lead insurer only has exposure to say 20%