If you're merely negligent, courts never award damages exceeding net worth, or as a business, its assets.
This is not true. The damages in negligence are based on making the Plaintiff whole. This applies even if the Plaintiff was already very susceptible to a serious injury etc.
http://en.wikipedia.org/wiki/Eggshell_skull You might be thinking of "punitive" damages where one factor is the ability of the defendant to pay.
There are 2 reasons an umbrella makes sense for someone with a higher net worth. 1) You can afford it. $300 a year on a high salary/net worth is not much. However, on a $30,000 a year salary, net worth you might be giving up something with a more immediate and guranteed benefit.
2) "Judgment Proof"/ "You can't get blood from a stone." Let say your vicous rottweiler bites your neighbor's kid's face off. Your homeowners has a $300,000 limit for liability. Their total damages awarded by a jury could be 1.3 million. If you make $30,000 a year, and have savings of $5,000 the Plaintiff's attorney might tell their client that they should take the "policy limits" because getting more from you is unlikely. But most lawyers don't want to go to the hassle of doing that to get $5,000 a year for the next 20 years until the jdugment expires. But if you have $100,000 in the bank, and make that much again each year, then they can garnish a much higher amount. It probably is worth it for them to seize the bank account. It might even be worth it for them to garnish your wages for 20 years at $25,000 a year to get $500,000.
People who are "judgment proof" don't need additional insurance because most lawyers aren't willing to spend $3000 to get $5000. But they are willing to spend $3,000 to get $150,000.
Also, the amount of equity in the home matters. Most states exempt some amount of value in a residence from a judgment. If your equity is below that amount, they can't seize the home. If you own your home free and clear, it might be seizable.