Dumebi Adigwe, a rising sophomore studying mathematics at Harvard University, has no idea where she is going to live. This week, Harvard announced it would allow only up to 40 percent of its nearly 6,800 undergraduates on campus in the fall, the vast majority of them freshmen, and that all classes would be held online.

Ms. Adigwe, 18, is on a full scholarship and is the first in her family to attend college. She recently left her childhood home, which she called a “toxic place,” and moved in with a friend, where she planned on staying only through the summer, hoping that Harvard would reopen its doors in some capacity.

“Now there is no going back to school, I don’t have anywhere to go actually,” she said.

For all college students, including and especially those from low-income backgrounds, the coronavirus has unraveled years of hard work and extracurricular hustle. Life on Harvard’s campus was meant to offer students the possibility of forming relationships with well-connected peers and professors, a social environment that could multiply opportunities. Now, the experience has narrowed into what is possible through a computer screen.

Princeton, Stanford, Johns Hopkins and other universities also announced reopening plans this week in which most classes would be held online. (According to The Chronicle of Higher Education, about 60 percent of colleges and universities are planning to allow all students back in classrooms.)

Harvard, which will continue to charge full tuition, has said it will allow students who cannot “progress academically” at home to return to campus in the fall. But its process for evaluating which students qualify is opaque. The form the school is using to assess requests to return asks students to check various boxes indicating challenges at their home, including whether they have a Windows or Macintosh computer and face food insecurity.

It reiterates multiple times that the number of people allowed back on campus will be limited, forcing many students into what they perceive as competition with each other over who has a more difficult life.

Students understand that campus life cannot return to normal, and that the coronavirus itself is in no way the fault of universities. But in interviews this week, Ms. Adigwe and more than a dozen of her peers expressed frustration at various aspects of the Harvard reopening plan — particularly, at the $5,000 “room and board” allowance Harvard will give to every student who is eligible for financial aid and who does not live on campus.

In many states, $5,000 spread over a semester is less than what someone would make from working a full-time minimum wage job. And the allowance does not correspond with what Harvard students have paid for room and board. (Last academic year, $17,682 for the full year — almost $9,000 a semester — according to the university’s website.)

Rachael Dane, a spokeswoman for Harvard College, said that the school acknowledged and accepted students’ frustration.

“We’re committed to working with students and we are doing that as they engage through the financial aid office,” she said.

Abby Lockhart-Calpito, 19, a rising sophomore, whose family has struggled with homelessness for much of her life, said she is worried that $5,000 won’t be enough to cover food and housing needs for the entire semester, especially without the on-campus jobs she had while living in the dorms; work is hard to find in the middle of a pandemic.

“I know that a majority of Harvard students have places to call home and comfortable spaces in which to do their work in, but that’s not the case for me and many others,” Ms. Lockhart-Calpito wrote in an email.

Hana Kiros, 20, a rising junior, said the $5,000 amount feels arbitrary — not correlated with the real cost of living for students and their families. “What could be a lifeline for students on full financial aid could be pocket change for students that barely make the financial aid cutoff,” she said.

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In response to Harvard’s announcements, some students said they are searching for cheap housing in the Midwest. Some are exploring a gap year. Some fear they will need to drop out of college completely. Many are organizing against what they perceive as the school’s lack of consideration for their basic needs.

“At Harvard, being in the dorms was a luxury,” Ms. Lockhart-Calpito wrote. “Now that I have to worry about my housing for the next year, I have been grappling with a lot of emotions.” She said she believes the college must account for the challenges facing first-generation, low-income students (often abbreviated F.G.L.I.). “Harvard needs to do better,” she wrote.

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Credit…Tony Luong for The New York Times

Harvard, founded in 1636, is the oldest university in the United States and in terms of the size of its endowment, the richest. It first adopted a significant financial aid program in 1934, and was early to shift to need-blind admission, meaning that students were accepted regardless of their financial circumstances.

In 2004, the school introduced a financial aid initiative that made tuition free for families making less than $40,000 a year. (That number is now $65,000).

Today, the school says that 55 percent of its students receive need-based scholarships and 20 percent receive full scholarships. (Full tuition is $49,653.)

“These students are at this point a very integral part of Harvard, how it sees itself, its student body and identity,” said Jerome Karabel, the author of “The Chosen: The Hidden History of Admission and Exclusion at Harvard, Yale and Princeton.”

But some scholars say a fundamental tension remains between the school’s explicit mission in the first centuries of its existence — to reproduce the white gentry by educating its sons — and its stated role now, as a beacon of diversity and democracy where a prestigious education is available to any and all who merit acceptance.

These diverse, often vulnerable students often appear in the school’s publicity material. They are held up as proof of Harvard’s egalitarian ethos, in which the very best students are accepted regardless of circumstance or background. But they are more vulnerable in a crisis.

Shortly after the coronavirus first forced students off campus this spring, Nicholas Wyville, a rising senior who lives in a rural Southern town without easy access to internet, told The Harvard Crimson that working remotely accelerates inequality.

“The only equalizer at Harvard is the fact that we all live together and have the same accommodation. We live together, we eat the same food, we have the same faculty resources,” Mr. Wyville said to The Crimson. “But if you take away campus living and residential life, then you take away that equalizer.”

The fact that Harvard will continue charging full tuition is evidence to frustrated students that the school believes that the coming year’s education will match the value of growing and learning in a campus community.

“Shifting online might not reduce the value of the Harvard College brand, but it does severely diminish, if not fully impede, our ability to make connections,” students said in a petition circulated this week calling on Harvard to provide more support to “low income students, working students and those with difficult home situations.” Ms. Dane said that the school had seen the petition but did not say whether it planned to respond.

Many who signed the petition think the school failed to prioritize outreach to its most vulnerable students. “I’m annoyed that figuring out the facts of what my options are for next semester has felt like a scavenger hunt,” Ms. Kiros wrote in an email.

Credit…Tony Luong for The New York Times

Silvana Gomez, a rising senior, said she began her time at Harvard “wide and bright eyed, thinking that this place is magical and amazing.” Now, she believes the school has failed her and others.

“It’s heartbreaking to feel like we’re not seen and we’re not really advocated for,” she said.

Ms. Adigwe, frustrated about the process of applying to get back to campus this fall, said: “You have to pimp out your trauma for them to even pretend to care about you.”

After Harvard’s announcement this week, students have been reaching out to college deans and the financial aid office to demand changes. This week’s student petition, which has more than 1,000 signatures, calls on Harvard to provide students who receive a full scholarship with “the full cost of living on-campus — $18,389 — and then potentially prorate that amount based on financial aid.”

There are also “very large group chats” of students planning action in the wake of the school’s decisions, Ms. Adigwe said.

The petition also called for structured support for international students, who have found themselves in the eye of a political hurricane. The same day that Harvard announced its plans for online classes, the Trump administration said that international students at American colleges would lose their F-1 visas if they did not take any in-person classes. Harvard and M.I.T. filed a lawsuit on Wednesday against the administration, contesting the rule.

Yousuf Bakshi, 18, a rising sophomore, was already dreading a full year of attending Harvard from home in Cardiff, Wales. The time zone difference, he said, is brutal. Last semester, his classes often continued until 3 or 4 in the morning. He lives in a small house with his parents and younger brother, and struggled not to disturb them while participating in discussions. “I kept waking up the whole house every single day,” he said.

Mr. Bakshi has a campus job that he’s able to do remotely. But he’s concerned that the new immigration policy may cost him the job if he loses his visa. “That will be really devastating because I’m really relying on that to financially afford being at home,” he said.

Lauren Marshall, 20, a rising junior who lives in Britain, is one student who is deeply concerned about the visa issue. “I don’t want to sound super-dramatic, but it will kind of change my life,” she said. Ms. Marshall and other students said that in a meeting on Wednesday, held with international students, Rakesh Khurana, the dean of Harvard College, said that the school is facing a “Sophie’s choice” between the health of the student community and international students.

Ms. Dane said that the comment was made in reference to “the Trump administration and the sense of urgency that was necessary.”

Harvard is allowing students to defer their education for one year, so many in the group chats are discussing that possibility as well.

Ms. Kiros is one of those weighing the option. “My life has just been blasted open,” she said. But she is also a first-generation American, and her parents “came to this country in part to, you know, give their children a better life,” Ms. Kiros said. “To them, a gap year or a gap semester is a pretty foreign concept.”

Penelope Alegria, 18, an incoming freshman, is torn between spending her first semester at school and remaining at home in Chicago. She really wants to make new friends and experience the campus.

If she does attend in person, however, the school’s stringent social distancing policies will render the semester unrecognizable from traditional freshman year frisbee-on-the-quad archetypes.

Ms. Alegria noted that the lack of communal spaces will be particularly tough. In information provided to students, Harvard said: “Most facilities such as common rooms, gyms, and large gathering spaces will not be open.”

“It really just sucks.” Ms. Alegria said. Besides, her parents, who are from Peru, would rather she stay home, and she knows how much they could use the $5,000. “They’re just kind of like, ‘Well, I mean, you’re still going to school, and they could possibly be giving you money to go to school, so, like, I don’t understand why you’re crying,’” she said.

Ms. Alegria finds solace in a group chat with other low-income freshmen, many of whom are also struggling with the decision. They take polls about which way they’re leaning. “The last poll was 24 votes for campus, six votes for home and three votes for elsewhere,” she said.

Ms. Gomez, who has been able to stay on campus this summer, said that F.G.L.I. students often can’t just remain at their “parents’ home for six months and become, you know, another burden on our on our family.” She added: “This is a very privileged thing for people to do.”

Some students fear that taking a gap year could cause them to lose access to scholarships and housing. Ms. Dane said that financial aid would not be revoked for any student in need but that housing was not guaranteed.

“We have given students an opportunity to make informed choices by sharing with them the context by which the university will allow them to return post-leave of absence,” she said. “They need to make an informed choice that is the best for them.”

Lucy Wickings, 20, a rising junior who has struggled with homelessness, pointed out that students who stay in dorms won’t get the $5,000 allowance. She has been living alone in her dorm free of charge since March, but she’ll have to petition the school to continue doing so in the fall and she’s not sure if she’ll bother.

“The meal plan in the spring was not sufficient,” she said, and she would “probably likely be paying for my own groceries still in the fall.” The three on-campus jobs she held before the pandemic would have helped with that, but their status is unknown. — .

Along with a few friends, she’s considering moving to the Midwest where the allowance will stretch farther. It’s not ideal, Ms. Wickings said, “but you know, we’re going to have to just do whatever we need to do.”

For Rani Shagarabi, 21, there’s no fixing what ails Harvard. The school, he believes, pays lip service to the needs of minorities and poor people while serving its own interests. “It’s the discrepancy between their words and their actions,” he said.

In May, he decided to drop out and stay home in Atlanta rather than return for his senior year, despite his full scholarship.