That's only if the judgement is AWARDED for punitive damages, which is rare. But if they are awarded, it's supposed to suck for you - that's why it's a punishment.
punitive damages are generally not awarded unless the courts see intentional acts that cause damages. Do not confuse punitive damages with general damages such as pain and suffering. Punitive damages are awarded to specifically punish egregious acts.
Insurance CAN'T cover punitive damages, if they did it wouldn't be punishment.
Now, want to tell us what happened?
Without the facts, there is no issue. If a theoretical opinion on punitive damages is appropriate, there are a lot of resources on-line. If different, provide the facts.
A judgment is good for 20 years so the judgment holder can take there time till you do have the funds.