For example, Warren McCleskey was convicted and sentenced to death when a cellmate testified that McCleskey had confessed to him. The snitch had been offered a deal for the testimony but when asked if there were any deals, the prosecutor said there were not. Ten years later, the lie was revealed. Unfortunately, it was too late for McCleskey. His case had already been through the federal court system and the Supreme Court held that he was not entitled to any additional appeals.
Prosecutors rely on the testimony of co-defendants, who also have strong motivation to lie.
For example, Justin Lee May was convicted of capital murder based on testimony made by his co-defendant, Richard Miles. In exchange for testifying that May pulled the trigger, Miles was allowed to plead guilty to a non-capital offense. All of my testimony was untrue. The police told me that I could be executed if I didn't cooperate, so I decided that if I didn't point the finger at May I would be executed. Fortunately for May, the Fifth Circuit stayed his execution giving him time to bring forward the new evidence of his innocence.