Insurance companies have insurance companies too. These are called reinsurance companies.
Buying reinsurance allows insurance companies to reduce the amount of risk they carry. The same way car insurance allows you to lower your risk of going broke because of a car accident, an insurance company will use reinsurance to lower its risk of going broke due to a run of bad luck, like a lot of clients getting into a bunch of car accidents all at once.
These reinsurance contracts commonly contain what's called an aggregate extension clause. These kinds of stipulations allow the purchaser to combine separate incidents into a single event for the purposes of figuring out its losses. Basically, the insurance covers a certain amount of loss, not a certain potential event.
If your car insurance worked a similar way, coverage might go something like this: instead of paying when you got in an accident, the insurance would kick in any time your car expenses went above a certain amount for the year.