This is why everyone needs an umbrella policy. It was actually cheaper to get a $5 million umbrella policy that boost my liability coverage on my cars and house.
Not everyone can qualify for an umbrella. Some companies require you have home owners and auto with them for the umbrella and your auto policy usually has to have minimum liability requirements of 300,000/500,000/100,000. If you have a dog that has bit anyone... ever, even once, you may be denied. DH had a backing accident; my son has two speeding tickets, and I had a tire fly off a semi truck in front of me on the highway that I couldn't avoid on I-75 rush hour traffic so filed a claim for the damage to my vehicle from the impact and was denied an umbrella based on driving history. I plan to reapply for an umbrella once my son goes onto his own policy and the backing accident should fall off next year. Umbrella polices are pretty strict on who they accept.
For anyone, you need to ensure your liability limits exceed your assets. If not, yes, you can be sued and could lose your home, retirement, future wages, etc. So many people do just want less expensive insurance and will take state minimum liability limits not realizing they are leaving themselves vulnerable for lawsuits.