André Leon Talley Reflected on Linda Evangelista's Mark on Fashion in Final Interview Before His Death

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In September 2017, in a flashback to the '90s supermodel era, Cindy Crawford, Claudia Schiffer, Helena Christensen and Naomi Campbell suddenly appeared on the Versace runway. The audience in Milan leaped to their feet with applause — while the audience on social media leaped into the comments: Where is Linda Evangelista?

She had been one of the so-called Big Five supermodels, and when she didn't show up on the Versace runway, it didn't take long for the paparazzi to find her. Tabloid headlines blared: Linda Evangelista Is Unrecognizable as She Jets Out of New York.

"They came for me," she remembers in this week's PEOPLE cover story. "They said I was 'unrecognizable,' and I didn't disagree with them."

For the full interview with supermodel Linda Evangelista, listen to today's special episode of PEOPLE Every Day, the daily podcast from PEOPLE:

What no one knew: She was keeping a painful secret. Now Evangelista, 56, is opening up exclusively to PEOPLE about the emotional and physical anguish she's endured for the past five years.

RELATED: Linda Evangelista Shares First Photos of Her Body Since Fat-Freezing Nightmare: 'I'm Done Hiding'

In a lawsuit filed in September, she alleges that CoolSculpting — popular, FDA-cleared "fat-freezing" procedure that's been promoted as a noninvasive alternative to liposuction — left her "permanently deformed" and "brutally disfigured" from the rare side effect paradoxical adipose hyperplasia, which affects less than 1 percent of CoolSculpting patients. According to her suit, she's been unable to work since undergoing treatments in 2015 and 2016, and she's suing CoolSculpting's parent company, Zeltiq Aesthetics Inc., for $50 million in damages. (CoolSculpting denies liability and says Evangelista knew the risks.)

"I loved being up on the catwalk. Now I dread running into someone I know," she tells PEOPLE.

RELATED: Original Supermodels Reunite for Walk Down Versace Runway 26 Years Later

One person who witnessed firsthand how much Evangelista loved being up on the runway was André Leon Talley. The former American Vogue creative director and author, who spoke to PEOPLE before he died in January, said, "You know Linda Evangelista [even] if you don't know fashion."

"You know the name Linda Evangelista. The way you know the name Cindy Crawford or Kate Moss or Naomi Campbell or Christy Turlington," he continued. "But any model that came before her, she surpassed them because there was something unique about Linda."

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Over her entire career, Talley was cheering her on at fashion shows, on shoots and in fittings with designers such as Karl Lagerfeld.

"Karl really adored Linda," Talley remembered of his time with the late Chanel designer in his Paris atelier. "He made sure she got very special looks."

Growing up near Niagara Falls in Canada, Evangelista dreamed of becoming a model and taped pages ripped from magazines of iconic '70s faces like Joan Severence and Janice Dickinson to her walls.

"I loved fashion so much," she tells PEOPLE. But for the middle child of three in a "blue collar" household (her father worked in a General Motors factory, her mother was a stenographer), the fashion world seemed out of reach.

"My parents were peasants who emigrated from Italy," she says. "We were taught to appreciate things like electricity and a toilet—and everyone worked two jobs." Including her. When she wasn't attending Catholic school, she worked on a farm, in a retail store and at the Hollywood Wax Museum in Niagara Falls.

"We were brought up to work hard to get what you want," says Evangelista.

RELATED: Supermodel Linda Evangelista Says She's Been 'Brutally Disfigured' by CoolSculpting Procedure Done 5 Years Ago

In 1977, a newspaper ad for a local modeling school caught her eye. That eventually led to the Miss Teen Niagara Pageant in 1981. She didn't win, but a scout from the prestigious Elite agency was in the audience. Evangelista landed her first job three years later, in an ad for hairstylist Jean Louis David.

"He cut my hair and photographed me," she recalls. "The cherry on top was that I got paid. I couldn't believe my big fortune." At age 19, she scored her first magazine cover. Talley recalled her rise to fame: "Linda had ambition—blind ambition. She went to school. She worked hard. She learned the craft. And she rose to the top."

"She wanted it," Talley said. "She wanted it like any great actress wanted to be Katharine Hepburn or Bette Davis. She was this constant professional. She always showed up with a smile, stood for fittings. And she just, she just made the designers feel so comfortable with her about the way she would express their clothes on her body."

RELATED: Linda Evangelista Says She Has 'Paradoxical Adipose Hyperplasia' from CoolSculpting: a Doctor Explains

Before long Evangelista was a runway favorite and became known as a chameleon. One season, long blonde hair. The next, short and red. Then a brown pixie. (That cut, in 1988, became known as "The Linda.")

"She could transfer herself into the personality that the particular designer or couturier wanted for that season," said Talley.

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And of Evangelista's infamous 1990 quote, which she told Vogue: "Christy and I, we have this saying, we don't wake up for less than $10,000 a day" — Talley says the greatest model of all time was simply ahead of her time.

"Back then, we dismissed it. I wasn't shocked," he said. "They were making that kind of money, you know? But today, it would be very relevant for a woman to say that, for proper equity. It would not be considered a snobbish, elitist thing. It would be considered, you know — She's a person of value speaking out for her rights."

But Evangelista wasn't simply posing — she was also involved behind-the-scenes as a fashion industry tastemaker with an eye for all things editorial.

"The joy and privilege of working with her," Vogue editor in Chief Anna Wintour tells PEOPLE, "was that Linda was as vital and collaborative as any photographer or editor to creating memorable images. It showed every time she was in front of a camera or walked the runway. Linda really does stand as one of the greatest — if not the greatest — models of all time."

For the full, exclusive interview with Linda Evangelista, pick up a copy of PEOPLE'S latest issue on newsstands Friday.