The prosecutor suppressed the statement by a guard who overheard Rhodes confess to two inmates.
Prosecutor lied saying he gave Rhodes the deal only because he passed a polygraph exam: the polygraph was a sham.
In Sonia's case, the jailhouse informant who later recanted said the prosecutor knew she, the snitch, was making it up.
In Jesse's case, the prosecutor came up with a bogus jailhouse snitch named as a witness on the first day of trial and failed to divulge facts about that witness' career as a snitch.
(State's Attorney Satz apparently has a habit of using jailhouse snitches in a large percentage of his cases.) In Sonia's case, the prosecutor failed to turn over the exculpatory polygraph summary.
Although the statement only directly exculpated Sonia, because Jesse and Sonia were linked by Rhodes' testimony, any evidence contradicting his trial testimony and showing him to be a liar would also have helped Jesse.