As previously undisclosed subpoena adds another angle to federal agents’ activity surrounding the longtime House speaker and chairman of the Democratic Party of Illinois.

“Revolving door” laws are intended to stop state lawmakers from getting private jobs after granting political favors. Illinois is one of the few states that does little to curb the practice.

Chicago is the most corrupt city, and Illinois the second-most corrupt state, in the nation, according to a recent report by the University of Illinois at Chicago. But corruption in Illinois is more than a buzzword. It comes with social and economic costs. Not only does corruption lessen residents’ faith in the government, it decreases...