Andrew J. Robinson, Garak's actor, details this in his novel A Stitch in Time. Which basically reveals all the backstory and mystery behind Garak.
Procal Dukat(our Dukat's father) was a Cardassian Chief Justice. He used his position to engage in various profitable criminal activities and shield himself from them.
Garak is the one who caught him, by earning his trust then betraying him, and Procal died by Garak's hand during the following interrogation.
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Procal Dukat was a male Cardassian in the early 24th century, the father of Skrain Dukat.
He was the head of the Cardassian court system with the rank of Chief Justice. He was very ambitious to further his career, and raised his son to be the same and to be a strong, capable man. Skrain loved his father very much, and Procal treasured his family dearly. Procal apparently furthered his ambitions by engaging in criminal activities, using his position and influence to shield him from the law. Needing proof, the Obsidian Order sent Elim Garak to gather evidence on Procal's secret activities. Garak managed to worm his way into Procal's inner circle by earning his trust and taking advantage of his short-sightedness. Garak exposed Procal's activities to the Cardassian Central Command, effectively ending Procal's career. After being arrested and put on trial, Procal claimed that his only flaw was that his ambition outweighed his patriotism, and was sent to prison for life. The Order sent Garak to interrogate Procal again, but Procal was able to resist Garak's torture methods and attacked him. Procal was killed by Garak in the ensuing scuffle. Skrain despised Garak from then on, which would last the rest of both their lives.