Scenario: Driving along a hilly, scenic highway, you're not really paying attention and drift ever so slightly over toward the line and the shoulder, striking a cyclist, breaking your side mirror and sending the athlete to the pavement. You pull over, call an ambulance (because leaving would only make your life worse at this point) and render what assistance you can until EMS and law enforcement arrives. On verifying (or, not) your proof of insurance, the officer informs you that you have no policy in force, and you now seem to recall that State Farm envelope among all the junk mail on your kitchen table - that you never opened - Yes, the one that said "Your policy will be cancelled in 10 days unless..." Besides the ticket for No Insurance, you now start getting calls and letters from the cyclist's insurance company who is seeking reimbursement from you for the $86,874.29 in medical expenses that they already paid for his injuries.
This, by the way, is called Subrogation, defined, essentially, as "The right of one [i.e. insurance company], who has paid an obligation which another [i.e. you] should have paid, to be indemnified by the other [you]". A variation of this example would be that the cyclist has no insurance at all, and the demand letters you receive are from the injured party's lawyer. That would not be Subrogation; however, the results are nearly the same - you are responsible to pay for the damages you caused, and now because your insurance wont defend or pay the claim, you are left to fight one or more insurance companies or lawyers on your own, or pay the demand out of your pocket. In some states, you may lose your license to drive until you pay, or are satisfactorily paying, what you owe. A lawyer experienced in defending people whose insurance coverage has lapsed can reduce your financial exposure. Often considerably. Sometimes totally.
The surest way to avoid financial disaster is to retain your own private counsel as soon as you know that 1) your insurance policy is insufficient to cover the expected claim, or 2) your insurance company has informed you that it will not defend the claim against you. Rare is a claim that cannot be defended and/or negotiated. Most likely, there are legal maneuvers and defenses that you have never considered, and a knowledgeable, experienced lawyer may save you tens of thousands of dollars or more.