There are UK universities facing deeper financial problems than at "any point in living memory", warns the head of a higher education think tank.
Nick Hillman, director of the Higher Education Policy Institute, says some universities are "close to the wall".
But the think tank says its survey of student attitudes raises dilemmas over how much information should be shared.
The vast majority of students - 97% - thought they should be told if their university was in financial trouble.
But 84% said they would be less likely to apply to a university that had admitted facing such difficulties.
This raised the risk that if a university admitted to financial problems it would be unable to recruit students and would be even more likely to be forced out of business.
Mr Hillman said it was important for the university sector to work out how it should respond to such problems - and how it would balance the need for transparency with avoiding putting institutions at even greater risk.
"Talking privately to people who advise universities, they will tell you that… there are some universities that are much, much closer to the wall than they've probably been at any point in living memory," said Mr Hillman.
He said universities needed to decide how they could share information and "talk about it in responsible ways".
There have been reports of several unnamed universities in England being in serious financial difficulties - and one university had to depend on a bailout from the Office for Students.
The institute's survey of students found that 77% would expect the government to intervene if their university faced cash problems and 51% would expect a refund on fees.
Proof of financial stability
Higher education experts have suggested that the most likely response to such a university collapse would be a merger with another university.
But only 32% of students would want that to be the outcome.
Rachel Hewitt, Hepi's director of policy, said the survey showed that publicising information about universities' vulnerability would have a "significant impact" on their ability to recruit.
"While there are legitimate reasons not to make public the names of those universities that are facing financial difficulties, students are very keen to have this information," she said.
The chief executive of the Office for Students, Nicola Dandridge, said all universities registering with the watchdog had to "demonstrate to us that they are financially viable and sustainable".
"Were we to have particular concerns about the financial sustainability or viability of a provider, we would impose a condition to their registration or otherwise intervene as a way of seeking to prevent a disorderly financial failure and to protect the interests of students," she said.
"None of the providers we have registered have been issued with such a condition."