A reinsurer would, of course, be crazy not to themselves be insured. So there must be companies that insure reinsurers, and then companies which insure companies which insure reinsurers. How deep does this rabbit hole go?
But for those without such a deep bench, they, like other commenters mentioned do a round robin sort of thing.
(I went with a bit more, because stocks are more volatile than cash.)
If they have to pay out on their reinsurance of your home policies the fact that you've reinsured their auto policies does not help them.
Someone has to insure their reinsurance of your home policies, don't they?
So there's a limit to how much they need to re-insure.
Someone already said that the rabbit hole ends with eg Berkshire Hathaway. But it also ends with eg (retail) investors who hold catastrophe bonds or shares of insurance companies.