NOVI, Mich.—A little more than four years ago, Kwame Kilpatrick—widely described as “Detroit’s disgraced former mayor”—was clinging to one small hope.

He had been convicted in a “pay to play” scandal that rocked the Motor City. It entangled more than 30 codefendants, including his father. The controversy cost Kilpatrick’s mother the congressional seat she had held for seven terms.