But what was Citi thinking, handing over $40,000 to an undergraduate who had already amassed debt well into the five figures? This was, in effect, a “no doc” or at least a “low doc” subprime mortgage loan.

A Citi spokesman declined to comment, even though Ms. Munna was willing to sign a waiver giving Citi permission to talk about her loans. Perhaps the bank worried that once it approved one loan, cutting her off would have led her to drop out or transfer and have trouble paying back the loan.

Today, someone like Ms. Munna might not qualify for the $40,000 she borrowed. But as the economy rebounds, there is little doubt that plenty of lenders will step forward to roll the dice on desperate students, especially because the students generally can’t get rid of the debt in bankruptcy court.

The University

The financial aid office often has the best picture of what students like Ms. Munna are up against, because they see their families’ financial situation splayed out on the federal financial aid form. So why didn’t N.Y.U. tell Ms. Munna that she simply did not belong there once she’d passed, say, $60,000 in total debt?

“Had somebody called me and said, ‘Do you have a clue where this is all headed?’, it would have been a slap in the face, but a slap in the face that I needed,” said Cathryn Munna. “When financial aid told her that they could get her $2,000 more in loans, they should have been saying ‘You are in deep doo-doo, little girl.’ ”

That’s not a role that the university wants to take on, though. “I think that would be completely inappropriate,” said Randall Deike, the vice president of enrollment management for N.Y.U., who oversees admissions and financial aid. “Some families will do whatever it takes for their son or daughter to be not just at N.Y.U., but any first-choice college. I’m not sure that’s always the best decision, but it’s one that they really have to make themselves.”

Image Citibank gave Cortney Munna $40,000 in loans, though she had already amassed debt well into the five figures. It was like the “no doc” loans that home buyers used to get in over their heads. Credit... Noah Berger for The New York Times

The complications here go well beyond the propriety of suggesting that a student enroll elsewhere. Colleges don’t always know how much debt its students are taking on, which makes it hard to offer good counsel. (N.Y.U. does appear to have known about all of Ms. Munna’s loans, though.)