Most likely your insurance company has refused to settle for the policy limit. If so, filing suit does 2 things:
1) protects the plaintiff from a statute of limitations bar on filing a suit (waiting too long is deadly to a claim); and
2) puts pressure on the insurance company to offer the policy limits.
Only where people have the bare minimum insurance to be legal to drive would anyone consider filing suit for more than the policy limits where there were grave injuries.
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As an example.
$25k policy limit. Plaintiff is paraplegic following accident that broke her neck. Defendant has assets.
But absent a scenario like that, the plaintiff will likely settle for policy limits.