Hard as it may be to believe, in Gyabaah v. Rivlab Transportation Corp. there is actually ongoing litigation before New York's appellate courts (this couldn't be resolved at the trial court level) over whether a personal injury case was settled. And it's still not resolved.
"How is that possible?" you ask.
Because a plaintiff was offered $1 million (the full value of the defendant's insurance policy) to settle her case, and, after signing the agreement, had second thoughts because she was concerned that she might be able to get more money than afforded by the insurance policy. That's when she hired another lawyer and tried to back out of the settlement agreement. (For more on this topic, please see "When a Personal Injury Case is Considered "Settled" Under New York Law").
At first blush, the plaintiff sounds terribly greedy - and that is certainly the way she was viewed by the dissenting judge in this case (who believed that the plaintiff should be bound to the settlement agreement that she signed). But, we don't know how much her injuries were actually worth, nor the circumstances under which she signed the agreement. That's why I don't think we should rush to judge her harshly.