I want to know if the car I'm renting comes with liability insurance. I just want to be sure that if I am at fault in an accident, that the other car will be covered. Lets try to ignore any personal car insurance policy and let's ignore collision insurance for now.

I am under the impression that in many countries they are required to give you liability insurance when you rent the car, but I don't have a good source. Many articles have mixed information.

For the US, this article says:

For a registered car rental company in the US, they must provide a minimum level of liability protection for cars they rent out.

But this other article says

In the U.S., every state requires a minimum amount of liability insurance on car insurance policies, so you may already have liability coverage through your personal auto insurance.

Which sounds like in the US your personal insurance is all you have.