With overcrowding in jails and new technologies that are able to overturn cases where innocent people were wrongly convicted, I think it is the governments duty to retrial more cases. This may cost money but we would also be saving money from imprisoning less people. And that is not to say that it is a moral duty to release falsely imprisoned people.
Routinely there is a news story about someone being let out of prison because they were wrongly convicted. Those cases are generally death penalty cases and high profile cases. Surely there are other innocent people in jail. It seems that the right thing to do is to at least do a random sampling and investigate lower profile cases and figure out whether wrongful convictions are prevalent.
Americans say that they would rather have 100 guilty men go free than convict an innocent man, but they do not mean it. Instead, judges and prosecutors just want to take the easy road out. They threaten people with life offenses in order to get people to agree to prison time. It is corruption at its finest.
More imprisonment cases do not need to be investigated by authorities. Although there have been high profile cases of false imprisonment, by and large, the justice system gets the decision right. Investigating a number of cases will cost a lot of money and place a large burden on the system.