Timothy Gregory Baldwin was convicted of murdering an 85-year-old woman and sentenced to death. He was executed in Louisiana in September 1984, between the execution of Pat Sonnier in April and Robert Lee Willie in December.
The most important thing about Baldwin, though, is that he was quite possibly innocent. Howard Marsellus, the Parole Board chief who was later convicted of bribery, tells Prejean that he had "grave misgivings about Baldwin's guilt" (8.102). He also says that the governor, Edwin Edwards, knew that the case against Baldwin was poor, and that he may have been innocent. The governor refused to pardon him anyway, for political reasons, and because the governor was kind of awful.
Baldwin, then, stands for the worst failures of the death penalty. Executing an innocent man is difficult to square with justice. Sonnier and Willie had at least participated in horrible crimes. Baldwin just was in the wrong place at the wrong time—and the justice system knew, and didn't care. His death is a symbol of the state completely mucking up, with horrible consequences.