Rubio's policies might shut the door to people like his grandfather

“It is ordered that the applicant be excluded and deported from the United States,” he said matter-of-factly, according to an audio recording of the proceedings stored by the National Archives. He stopped to ask if Mr. Garcia understood.

“Yes, I do,” Mr. Garcia said plaintively.

That easily could have been the end of his American story. But someone in the immigration office on Biscayne Boulevard that day — the paperwork does not make clear exactly who or why — had a change of heart. Mr. Garcia was granted status as a parolee, a gray area of the law that meant he would not get a green card but could remain in the United States.

As he campaigns for president, Mr. Rubio, a Florida senator, says that the United States cannot accept refugees from Syria and Iraq because of the potential security risk. More broadly, he has called for a tightening of immigration law so that if the United States cannot identify with 100 percent certainty who immigrants are and why they want to enter, he says, “We’re not going to let you in.”

But under the stricter screening he now supports, his grandfather would most likely have been deported, depriving him of knowing the man he has called his mentor and closest boyhood friend.