In New Haven, Conn., the school’s conspicuous absence from the crosshairs has become a subject of intense campus speculation—among professors, students and even parents. “This is the $64,000 question," said Evan Morris, a Yale professor of radiology and biomedical imaging. “My colleagues and I are all looking at each other and waiting for the other shoe to drop." The question hung over October’s Yale Family Weekend, as parents partook of cherished traditions like performances by the Yale Glee Club, lectures by distinguished faculty and tours of the neo-Gothic-style campus. During a talk with moms and dads, university President Maurie McInnis...