If the charges against Mr. Shkreli are true, his flunking out of Hunter, the prestigious Upper East Side school known for its Ivy League-bound students, was just the first in a series of failures that he would try to overcome with money, his own or other people’s.

Though he eventually graduated from another city high school, it was Hunter that seemed to have a hold on him. Classmates describe him as always offering to pay for nights out during their college years, giving the impression that he wanted badly to prove that he had made good. Then came his donation to Hunter. And then on Monday, in the days before his arrest, he drew more attention to his Hunter connection by chatting online with a female Hunter student during a live stream on YouTube.

The interaction transfixed the student body, many of whom abandoned their homework to watch the video, drawn by a torrent of messages on social media.

Casey Liu, 14, a freshman, said Friday she had found out about the event after a couple of her friends sent her snippets of it on Snapchat. Like much of the school, she and her friends have been talking about it since.

“They don’t like Martin, first of all,” she said. “They thought his live stream was a joke.”

She also said she thought the school should give back his donation. “He just seems like not a nice person,” she said.