There is not absolute answer to this question. If the individual was convicted of the crime and executed, his or her case is closed. There is no national standard that requires that the case be reopened or that any other action be taken. In some cases, the Governor, at the request of the family or the attorneys, can issue a pardon for the deceased individual, but there is no specific rule requiring this. There have been a few of these pardons issued by Governor's for individuals who were lynched when they were actually innocent of any crime. The problem with issuing some form of national requirement for this type of situation is based on money. If the family of the deceased were to receive a clear statement that the individual had been executed in error, it would open the government up to significant liability for wrongful execution or miscarriage of justice. The issue also comes down to the basis for the determination that the executed individual was innocent. If an eye witness later admits that they were mistaken or that they lied, the question is raised whether they were telling the truth the first time or whether they are telling the truth now. Some witnesses are certain that they are correct, but when they find out that thier testimony send someone to a death penalty, they start ot feel guilt and they become less certain of their testimony. The American system of justice is pretty good, but not perfect. We haev numerous appeals that can be raised and the convicted party can appeal the case over and over again. In most European countries, the death penalty no longer applies. But their system of justice assumes that the accussed in guilty until they prove themselves to be innocent and all of the burden of proof is on the accused. If they are convicted, they only have one appeal. After that, the now convicted individual completes their entire sentence before they are released. So, the correct answer is that there is no correct answer. The Federal Government has not addressed the issue to make a national standard, and the individual states are handling things in different way. The State of Illinois has ended executions until they develop some better way to determine if the penalty fits the crime and whether their system addresses the issue and provides all the safeguards that are needed to ensure that no innocent individual is executed.