A ringleader in one of the biggest Social Security disability fraud cases in U.S. history has pleaded guilty to filing more than 1,700 bogus applications, bilking the government out of potentially a half-billion dollars. But the administration is struggling to figure out how to handle the applicants, many of whom say that even though their applications were falsified, their cases are real and they shouldn’t be punished for having been ensnared by the massive fraud. Eric C. Conn, a prominent lawyer in eastern Kentucky, signed a guilty plea late last month acknowledging the scam, in which he recruited and filed...