How old are you, or, how close are you to FIRE?
Worst case scenario is an accident that leaves you with large, ongoing medical expenses and prevents you from working. Let's say that either you were at fault and uninsured, or the at-fault driver was uninsured and you didn't have any coverage for yourself (UM/UIM or PIP), so you're SOL. What would you need?
Well, if you're FIRE, not much. You would probably qualify for Social Security Disability Insurance (assuming you participated in SS while working), which would be income you weren't planning on getting before the accident, AND you'd be eligible for Medicare after two years of SSDI, so that takes health care costs out of your budget. You'd probably have some increases costs of living (can't bike everywhere because of injuries, need new house to accommodate a wheelchair, possibly need home health aides), but other costs would likely be lower (travel?), so you could probably find a way to work everything out without any insurance payments. And since my motto is don't insure what you can afford to replace, I would probably say you'd be good with just the minimum liability.
But you say you have a net worth of $35k, so I'm going to take from that that you're not close to FIRE. If you couldn't work and had large, ongoing medical expenses, what would you need?
Well, you'd need a few months of living expenses while you qualified for SSDI, if you even qualified. You have to have paid enough into the system to collect SSDI, so if you're very early in your career, you might not get anything. If your health insurance is from your employer and you can't work, you'd need money to pay for COBRA and then individual insurance until you could qualify for Medicare or Medicaid. You'd need living expenses for the rest of your life, less any SSDI you could get.
If you can get SSDI, let's say for the sake of argument that you get 30% of your prior income, and it takes 6 months for your application to be processed. Let's also say that before you were injured you were saving 50% of your income but paying nothing for insurance.
You'd need: 50% of 6 months of your current income to match your prior living expenses, plus 2 years of health care expenses, plus 20% of income to supplement your disability income for the rest of your life. Let's us the 4% rule for that last piece: to get .2X forever, you'd need 5X today.
.5*60k/2 + (ballpark) 15,000 + 5(60k) = 330,000
Let's say that you can't qualify for SSDI. Then you need half your salary, forever, plus medical expenses, which will depend on your state's availability for Medicare.
30/0.04 = $750k plus medical.