A Harvard spokeswoman declined to make administrators available to answer questions about the master’s degrees and the institute. Robin Kelsey, dean of arts and humanities at Harvard, issued a statement in which he expressed support for Ms. Paulus. He wrote, “Pausing the Institute will enable Ms. Paulus and her colleagues at the A.R.T. and elsewhere at Harvard to consider new and creative ways to support our shared pursuit of the dramatic arts.”

The institute’s relationship with Harvard is convoluted, which some students say is a cause of their frustrations. The institute is housed within American Repertory Theater, but from 1999 to 2016, students were granted master of fine arts degrees through Moscow Art Theater School, where they do a three-month residency. Starting with the class that graduated in 2017, however, students are being granted a master of liberal arts degree through the Harvard Extension School, a division that also includes open-access online courses like “Masterpieces of World Literature.”

With the exception of a small fund that distributes scholarships, institute students are not eligible for financial aid grants through Harvard. Me’Lisa Sellers, who will graduate in 2018 with roughly $135,000 in debt, said that she once went to a Harvard financial aid office in desperation. She recalled that an employee there asked her, “And this is a Harvard program?”

Institute students are given Harvard IDs and can live in Harvard graduate housing. But when one current student, Shawn Jain, went to join a campus gym, workers at the front desk had to look deep into the computer system to find him. Mr. Jain and Ms. Sellers also said they were initially denied access to discounted transit passes because they were told that they had to be administered through Harvard’s 13 schools, and the institute didn’t count. Though they were eventually given passes, it contributed to Mr. Jain’s sense of being a second-class citizen at Harvard.

“I feel like we’re the stepchild that no one really wants,” Mr. Jain said.