Shortly before he was fired as the Philadelphia Housing Authority's executive director in September, Carl R. Greene was hard at work building his newest nonprofit, the Pennsylvania Association of Public Service Agencies. It had the laudatory, but vague, mission of helping the region's public agencies save money through shared services and best practices. Now it is unraveling as federal auditors examine PHA's books and officials at the U.S. Department of Housing and Urban Development say federal money appears to have been misspent. Greene, fired for failing to report a series of sexual-harassment claims against him, is PAPSA's president. He was...