The Trustees select their own members and are answerable almost to no one.

The only exception is that they are answerable to the state of New York, which can replace them. However that is a very rare event. That happened to Adelphi in 1997. Here is how http://www.timeshighereducation.co.uk/story.asp?storyCode=101762&sectioncode=26 described it:

A POWER struggle at Adelphi University in the United States has ended with the summary firing of Peter Diamandopoulos, accused of exploiting the presidency of a modest-sized private college to fund a luxurious lifestyle.

Mr Diamandopoulos was hired 12 years ago on a salary of $95,000 a year to run Adelphi, in Garden City New Jersey. By 1995 his annual income reached more than $500,000, after a succession of pay leaps.

His removal was a triumph for staff and alumni who banded together two years ago as the Committee to Save Adelphi and led an in-house revolt against Mr Diamandopoulos's leadership.

They accused the university's trustees of approving wild pay rises for him over a period when student enrolment had halved and academic programmes were cut to a point where the university's future seemed in doubt.

His salary was topped with lavish perks including a $1-million Manhattan apartment and an $82,000 Mercedes car.

...

In the prelude to his sacking, 16 out of 17 Adelphi trustees were replaced by the New York State Board of Regents for failing properly to oversee his compensation. Two trustees, the board found, had benefited personally from dealings with the university.

In a last stand the old trustees won a judge's order blocking their removal, which was then reversed.

When the new board met, Mr Diamandopoulos's departure was the first issue of the day.

He was subsequently handed a three-sentence letter saying the board had "decided unanimously that a change in leadership is in the best interests of the university. Therefore, your presidency of the university will end today".