In many (most?) jurisdictions you can post a bond for liability insurance. This is typically used by fleet managers etc, but is also available to HNW individuals.
Essentially you prove to an insurer (by posting a bond) that you can and will pay for any third party damage you cause, and in return they give you a practically free (or cheap, super-high-deductible) policy.
In the UK you can post a bond in lieu of having motor insurance, but it's something like £250,000 so rather out of the range of the ordinary car driver. (It's mainly used for commercial vehicle fleets as you say.)
Essentially you prove to an insurer (by posting a bond) that you can and will pay for any third party damage you cause, and in return they give you a practically free (or cheap, super-high-deductible) policy.