Can you get auto insurance if you do not own a car?

Yes you can, it's called a named non-owned policy. It covers you to drive a vehicle you do not own, and it only covers you to drive a vehicle that does not have insurance. If you borrow a friends car and have a name non-woned vehicle and have an accident, the insurance follows the vehicle, so their insurance will pay. That company may subrogate and come after you then it would be up to your insurance company to decide if they'd accept liability.