In aviation, there is no legal requirement to have insurance. So anyone with the appropriate ratings for the type on their license could fly the aircraft, albeit uninsured. Whether you, as the owner, would be happy with that is your call.
I'm not aware of any insurance policies which cover you for any aircraft as many car insurance policies do. I suspect that if you wanted to be insured, short-term, on an aircraft, you'd need to be added to the policy as a named pilot. Depending on the type and the pilot's experience, the insurance company might insist on some dual before they'll do this.
That's my experience, anyway, but I've never dealt directly with aircraft insurance, only through my group's financial coordinator, so I may be wrong.
FFF
----------------