Baylor has a zero-interest-loan program for students who have exhausted other options, including Parent Plus, but that pot of money is limited, according to the school. Baylor says the college doesn't offer scholarships that are contingent on Plus denial, and students are able to appeal their financial aid offers regardless of whether they are rejected for the loan.

The federal government also increases the maximum amount students can borrow if their parents can't get Plus loans.

Ms. Heckel's parents were approved for the Plus loan and took on about $75,000 in loans on top of the nearly $28,000 that Ms. Heckel borrowed directly. Now in medical school, she has been helping her parents pay down the parent loan. She says she had a great experience at Baylor but navigating financial aid was difficult.

Parent Plus loans play a big role at Baylor in part because the school on average gives enough financial aid to cover only roughly two-thirds of what students whom it deems needy can pay, according to forms that many schools file. The majority of wealthy colleges cover it all, on average.

Only two other colleges in the Journal's analysis of available forms covered less than 70% of what students needed in financial aid: NYU and Baylor athletic rival Texas Christian University. At those schools, parents of recent graduates who used Plus loans took a median $74,000 and $57,000, respectively, among the highest amounts in the country.

NYU's Mr. Beckman said its median Parent Plus debt has been declining and the school expects that trend to continue. A TCU spokeswoman said the university is committed to making the school more accessible and in 2020 committed to increasing financial aid by $65 million annually in part to support current students and reduce loan debt.

Dr. Livingstone said that while Baylor has a large endowment, it has more students than some other wealthy colleges and so must spread the money further. Its enrollment, including graduate students, is nearly 21,000, roughly double from 1980. She said the school should be better equipped to help low-income students through current fundraising efforts.

Joining the elite

Behind the rise in Parent Plus loans at Baylor is the school's expensive campaign to join the nation's elite campuses -- and the rising tuition to pay for it.

Generations of Baptists sent their children to the college with a history of conservatism. Dancing wasn't allowed on campus until 1996. The percentage who identify as Baptist has dropped over time.

Baylor in 2002 embarked on a 10-year improvement plan to help become an elite school. Baylor financed much of it, according to university information online, by "substantial increases in undergraduate tuition and accessing the institution's previously under-utilized debt capacity."

The school issued about $247 million in bonds in 2002 to help pay for construction projects, which some alumni members criticized, fearing tuition would skyrocket to help pay for the debt.

Prospective students now fall in love during visits to the campus, gleaming with steeples and showcasing an enclosure with real bears, the school mascot. Sports have been a big draw. On the edge of campus sits the $266 million football stadium, which opened in 2014, also financed partly through debt. Baylor received a wave of attention after winning the NCAA Men's basketball tournament for the first time in April.

This fall, Baylor enrolled its largest freshman class ever, nearly 4,300 students. It now ranks 75th among hundreds of universities in the U.S. News & World Report rankings, up from 125th three decades ago.

Baylor used the U.S. News metrics as a blueprint in its quest to be a top-tier research institution, according to a university report. That has meant wooing students with high grades and test scores -- devoting scholarships to these often-high-income students, while leaving many poor students cash-strapped.

Last school year, Baylor gave $100 million to students based on considerations other than financial need -- 37% of its total scholarship budget. Dr. Livingstone said that the school uses merit scholarships to build a diverse class and that students with financial need get some of this money.

The practice is uncommon at the wealthy schools the Journal examined, most of which devoted less than 10% of aid to scholarships that didn't take need into account.

"They've priced themselves out of the market for the people that the founders intended them to serve," such as those wanting to be teachers and social workers, said 1967 Baylor graduate Bette McCall Miller, daughter of one of Baylor's longest serving presidents, Abner McCall. "Out of a group of 30 of us who went to Baylor and keep in touch, one or two would be able to go to Baylor today."

Dr. Livingstone said Baylor's current strategic plan has been funded without significant burden on undergraduate tuition and is supported by fundraising. She said that she is working to keep tuition increases low and raise funds for more scholarships.

Baylor's tuition and fees increased 2% this school year. They have increased by about 4% each of the past few years -- lower than previous years but roughly double inflation, published figures show.

'Good debt'

Parents with Plus loans can be stuck with payments for years. The loans aren't eligible for federal student plans that tie monthly payments to income and forgive debts after 20 to 25 years, though savvy families can get around that rule by asking the government to consolidate old loans into new ones.

Parent Plus loans can be discharged upon death or permanent disability of the borrower, as Kayla Foots discovered. The 2014 Baylor graduate said that about $100,000 in Parent Plus debt her stepfather took out was wiped away when he died last year. "That is so crazy and so sad that that was the silver lining out of the situation," said Ms. Foots, 30, a fashion buyer in Boston who said she makes about $55,000 a year.

Ms. Foots, the first person in her family to attend a four-year college, still owes roughly $66,000 on her own student loans. Her mother, a school bus driver, owes about $57,000 from borrowing Parent Plus loans for Ms. Foots.

In 2018 and 2019, Baylor parents who were supposed to begin repaying Plus loans a decade prior collectively owed 74% of what they borrowed. Parents at the wealthy schools in the Journal's analysis still owed 62%, on average.

Those who default on loans risk having wages garnished, including Ashley Massey's father. Ms. Massey, a 2009 Baylor graduate, said the federal government tapped his paycheck for not paying on his parent loan. Baylor's financial-aid office, she said, had advised the family to apply.

"It was a killer," said Jeff Stone, Ms. Massey's father, adding that his wages were garnished at $800 a month over two years. The retired firefighter, who now works at a fire-and-safety company, said he had since paid off the loan. He said that he didn't know much about the loan, until his daughter needed it, or how the repayment worked and was caught off-guard with the garnishment.

Ms. Massey, now a behavior analyst with a master's degree, still owes about $67,000 for a Baylor undergraduate degree. She said she now makes $81,000 a year and enjoyed Baylor but, given a do-over, would complete two years of community college to cut costs.

"They told me it was 'good debt' -- that it will pay itself off," Ms. Massey said of family members who encouraged her to attend Baylor. "I honestly haven't found anybody that cares about where I went to school."

Write to Tawnell D. Hobbs at Tawnell.Hobbs@wsj.com and Andrea Fuller at andrea.fuller@wsj.com