Melinda Allen could easily have fallen through the cracks at any college or university. She took time off from school when her parents died, exhausted all of her federal grant aid, owed unpaid tuition and became a mother when she was two years shy of graduation.

Allen’s academic advisers and professors at Dillard University in New Orleans refused to let her walk away from her education, she said. As she approached the limit on borrowing from the federal government in the fall, a ­financial-aid officer at the historically black university urged Allen, 29, to apply for a school grant designed to keep students like her from flaming out.

The $5,650 grant Allen received from the Student Aid for Financial Emergencies (SAFE) Fund has helped cover her spring classes, freeing up the money she earns working at a local theater to pay for child care and pay down her tuition balance.

“Even with me having this balance, they’re like: ‘The first step is reapplying, getting in here. We can figure this out. We can find some money,’ ” said Allen, a junior studying theater arts. “There are all of these different people [at Dillard] who want to help and see me succeed.”

Dillard, like many historically black colleges and universities, or HBCUs, is fighting to help its students reduce the need to borrow and keep them from joining the scores of Americans with debt and no degree. But how can schools with few financial resources help students in the same boat?

“You’re talking about under-resourced institutions that serve under-resourced people,” Dillard President Walter M. Kimbrough said. “A lot of times people are just trying to figure out how do we keep functioning as an institution and help students get the ­resources that they need.”

Even relatively wealthy black schools, such as Howard University or Spelman College, face the challenge of educating a large number of disadvantaged students with a fraction of the budget of comparable predominantly white colleges.

Historically black colleges, after generations of inequitable funding, lack substantial endowments to provide generous scholarships but serve a population in dire need of financial support. Without that assistance, their students rely heavily on loans that can exacerbate racial wealth disparities by making it more difficult to save and invest. The financial instability also places students at great risk of dropping out.

Schools have been experimenting with initiatives to keep students in college without saddling them and their families with more debt than they can ever repay. Some programs are as simple as providing a few hundred dollars in emergency grant aid, while others involve radical changes to the way the school operates.

The stakes are high for the schools and their students.

One in 4 students at historically black institutions borrow $40,000 or more to attend, according to the United Negro College Fund. Data from the Education Department shows HBCU students are more likely to struggle to pay down that debt and default on their loans than their peers — making their pursuit of higher education a gamble.

Institutions with a rich history of lifting African Americans into the middle class are not keen on contributing to the erosion of those gains.

But some of the nation’s 100 historically black schools are contending with their own financial struggles, with paltry private investment and fluctuations in crucial state and federal dollars. Many are reliant on tuition to keep the doors open, making them particularly vulnerable when enrollment wanes or students are unable to pay.

Kimbrough built up the SAFE Fund, which launched in 2013 with a $50,000 donation from the Delta Sigma Theta sorority, while Dillard was still reeling from the devastation of Hurricane Katrina. The storm damaged buildings on campus, leading Dillard to borrow money from the U.S. Education Department that it struggled to repay amid tepid enrollment.

The loans have since been forgiven. The university is on better footing, and the SAFE Fund continues to draw donations. Still, the experience demonstrates an all-too-common challenge for historically black schools — lacking a safety net to weather crises or meet the tremendous financial need of their students, but trying to do both at the same time.

“You have a unique population of students, and you also have institutions that can’t pull from financial resources to support them like other types of schools,” said Krystal L. Williams, an HBCU expert and assistant professor at the University of Alabama. “There has been historic and unequal consideration for funding by corporations and foundations.”

To an extent, that has begun to change. Howard University in Northwest Washington has scored sizable donations lately, including $10­ ­million from the Karsh Family Foundation to fund a science and technology scholars program. It is the largest gift in the private university’s 153-year history, but it pales when compared with the tens of millions of dollars that neighboring Georgetown and George Washington universities have secured.

Still, the donation will allow Howard to support students who often have enough financial need to receive Pell Grants, a federal program for students whose families typically earn less than $50,000 a year.

Nearly half of undergraduate students at the historically black university are eligible for Pell, and just as many borrow to finance their education, owing an average of more than $20,000 at graduation.

Even as the school worked to reverse years of financial strain, Howard President Wayne A.I. Frederick introduced tuition assistance programs and financial incentives to get students out the door faster — while they spend less on their degree.

Students in good financial standing can take up to six credits during the summer free, and those who graduate within four years are eligible for a tuition refund. Frederick credits the initiatives with raising the school’s four-year graduation rate from 38 percent to 52 percent since 2014.

“We’re starting to see a lot more donations, a lot more interest because of these innovations,” Frederick said. “People are seeing the results and paying attention.”

Howard also covers the remaining tuition and fees for high-achieving students such as Amari Michaux who receive the maximum Pell award — $6,195 for the 2019-2020 academic year. Thanks to the $20,000 Michaux receives from the school, federal grants, assistance from his grandmother and a few outside scholarships, the 20-year-old biology major has not taken out loans.

“I knew I had the grades to get in but not the money,” Michaux said. “My education is probably the most important thing to my grandma, so she was talking about taking money out of her 401(k) for me to go to school. It’s a blessing to have this help.”

At Lane College in Jackson, Tenn., freshman Lariyana Boyd, 18, can also forgo loans to earn a degree in business administration, because of a new program for low-income students with stellar grades. After state scholarships and federal grant aid are applied, the historically black school is covering the remaining cost of attendance for Boyd and 21 of her classmates.

Although Lane has received $100,000 from the Coca-Cola Foundation to support the program, the school is footing most of the bill for choosing not to collect tuition from the scholars. The discount strategy is a bet the students will remain in school, bringing in revenue from state and federal aid, said Lane President Logan Hampton.

Tapping the college’s $5 million endowment to support the program was not feasible. Lane, founded in 1882 by a formerly enslaved preacher, is the kind of school where everyone on staff has more than one job and where the president insists on switching to LED lightbulbs to save money.

“We can’t focus on our deficits,” Hampton said. “Ninety percent of our students are Pell-eligible. They arrive with underdeveloped academic skills, trauma . . . needing every resource we can provide. It is our obligation to assist them.”

It is a sentiment shared by Michael J. Sorrell, president of Paul Quinn College in Dallas. He took the helm at the historically black school in 2007 when it was on the brink of bankruptcy, but Sorrell refused to repair Paul Quinn’s finances on the backs of its students.

“The idea that you would leave students and their families with enormous debt burdens just because that’s what it takes for you as an institution to meet your bottom line just seems morally reprehensible,” Sorrell said. “People deserve better.”

Sorrell ended the football program, renegotiated contracts, took a 25 percent pay cut and asked administrators and faculty members to take temporary pay cuts of up to 20 percent to help turn around the college. In a counterintuitive move for a school engulfed in financial turmoil, Sorrel cut tuition by 40 percent — from $23,800 to $14,275 — to make it easier for students to graduate with minimal debt.

His boldest move came in 2013 — requiring all students to work, first on campus and then in the community. Students keep a portion of their pay and use the rest to defray the cost of attendance. The urban work-college model has been so successful that the school is opening a second campus in Plano, Tex., and partnering with JPMorgan Chase, FedEx and others to sponsor internships.

The model gave Vincent Owoseni, 24, an opportunity to intern at a private-equity firm in 2016, setting him on the path to his current job in the field. The 2018 graduate attended Paul Quinn while it was in the throes of transformation and says he still holds dear Sorrell’s motto of “We Over Me,” which is written on a note affixed to his computer.

“Paul Quinn taught me that the skills that you acquire and develop are not just to benefit you. . . . You’re supposed to use that to benefit the world at large,” Owoseni said. “That’s the biggest takeaway from my education.”