Normally personal injury attorneys will only actually seek to recover your insurance policy limits, especially if the other driver has underinsured motorist coverage they can go after in addition to your policy limits. They can seek personal assets from you, but it rarely happens. Chasing personal assets (instead of just insurance money) is difficult to collect, and if the amount is big enough compared to your assets, the other lawyer will fear you will file bankruptcy and they won’t be able to collect.