There are many people way more qualified to answer these questions than I , but here is my amateur take on it.
One of dirty secrets of injury insurance and part of the reason health insurance is so expensive is when someone injured, their health insurance will take the major hit for medical bills. Then the insurance company will go after any injury insurance any involved parties have, Usually but not always this money get split 3 ways between the injured party, the Lawyers, and the Medical insurance company.
If have a client that you know does not have medical insurance, you may want to counsel them and/or not fly with them as they are essentially uncovered for any major medical injury.
Again strongly recommend professional advice.
But generally your primary house and your 401K are protected from litigation. So your liability/injury insurance should be enough to cover any remaining assets you have to make it more attractive for a litigant to take the insurances money and run rather than go after your assets and have the insurance company use your insurance money to defend you.
Brian