I am a lawyer, and I dealt with this all the time. (Criminal defendants have a habit of dying young)

A criminal judgment is not final until the Judgment of Sentence is imposed. If a defendant dies before sentence is imposed, the charges are dropped and he dies without a conviction on his record.

If a defendant is convicted and sentenced, but dies while his appeal is pending, the sentence is not considered final (even though it is being served) and, again, he dies without a conviction on his record.

In a civil case (a lawsuit), the estate is substituted for any party that dies, whether plaintiff or defendant. Even if someone who did wrong dies before suit is brought, the lawsuit is brought against his or her estate. Likewise, if you die due to someone's negligence before a lawsuit is filed, the case is filed by your estate against the wrongdoer.