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Mr. Crowley recalled a 2009 trip to Pakistan during which Mrs. Clinton took part in a roundtable discussion with news anchors from Pakistani television. “In the aftermath, the reaction had one person being quoted in the major daily papers in Pakistan as saying ‘our leaders don’t talk to us the way that she just talked to us,’” he said.

“She was setting a standard in terms of how leaders should engage citizens of the world,” Mr. Crowley said, adding that Mrs. Clinton was alternatively tough in meetings with the Pakistani media before the May 2011 Navy SEAL raid that killed Osama bin Laden in Pakistan.

During one exchange, a group of Pakistani newspaper editors was hounding her about restrictions on U.S. aid to Pakistan, Mr. Crowley said. “She responded by saying, ‘Hey, you’ve got questions for us, well, we’ve got questions for you. It’s hard for us to believe that no one in Pakistan knows where Osama bin Laden is.’”

Others say Mrs. Clinton’s legacy will be one of a secretary of state who honestly cared little about what her legacy would be.

Michael O’Hanlon, a senior fellow at the Brookings Institution, said she is a leader who “works her tail off” and puts the pursuit of positive results well above that of praise, approval or fame.

“She has been solid, pragmatic and diligent as opposed to flashy, risk-taking or otherwise preoccupied by her image of herself and her place in history,” Mr. O’Hanlon said. “I don’t think she spent a lot of time on that. I think she spent a lot of time trying to understand how to solve problems.”