Virtually every car rental company will allow you to buy liability insurance which will protect you in the case that someone makes a claim against you for personal death or injury or property damage.
Sometimes it doesn't have an obvious name: Hertz calls it Liability Insurance Supplement and Avis Legal Liability, Third Party and Public Liability Cover. It is often described as coverage additional to your personal liability coverage but it can be bought if you have no coverage of your own.
Availability and details can vary hugely between states. In many states liability coverage must be included in the rental car price. In others you have to pay extra for it. A price of around $15-$30 a day seems fairly normal, but it varies a lot. I obtained a quote from Hertz at Minnesota St Paul's airport that charged $161 for supplementary liability insurance for a 7 day rental.
When you are considering car rental you should therefore 1) check to see if liability coverage is included in rental prices by law in the state where you want to do the rental 2) check with each car company to see what the price of the liability coverage is. This can almost always be done as part of the online booking process. Booking online for a specific location will also let you know if the product is available at your location.
Note that this is a different coverage from LDW and CDW (Loss/Collision Damage Waiver) and only protects you from claims made by other people.