Ms Borders, a mother of two, died on Monday, her family said on Facebook.
She blamed her cancer on inhaling dust during the attack and suffered from alcoholism and anxiety in later years.
"I can`t believe my sister is gone," her brother Michael Borders wrote on Facebook. Her cousin John Borders called her a "hero" and said she had "succumbed to the diseases that [had] ridden her body since 9/11".
"In addition to losing so many friends, co-workers and colleagues on and after that tragic day ... the pains from yesteryear have found a way to resurface," he added.
On 11 September 2001, Ms Borders was just one month into a new job at Bank of America on the 81st floor of the north tower when the plane hit.
"The building started quaking and swaying. I lost all control, and I went into a frenzy. I fought my way out of that place," she told the Daily Mail in 2011.
Defying instructions from her boss to stay put, she fled down the stairway and into the lobby of an adjacent building where she was photographed by Stan Honda.
Marcy Borders (R), survivor of the 11 September attack on the World Trade Center, sits with photographer Stan Honda (L), 08 March, 2002,
Mr Honda recalled the moment in a post on Facebook on the 10th anniversary of the attacks.
"A woman came in completely covered in grey dust. You could tell she was nicely dressed for work and for a second she stood in the lobby. I took one shot of her before the police officer started to direct people up a set of stairs, thinking it would be safer off the ground level."
Ms Borders, who was from New Jersey, was not aware she had been photographed until her mother saw the image the following day and contacted the Mr Honda.
In the years after the attacks, as her picture became one of those most iconic images of the day, Ms Borders suffered from severe depression and drug addiction and lost custody of her two children.
"I didn`t do a day`s work in nearly 10 years and by 2011 I was a complete mess," she told The New York Post in the same year. "Every time I saw an aircraft, I panicked."
But after a spell in rehab starting in April that year, she became sober and regained custody. Then in November 2014 she revealed that she had stomach cancer.
Ms Borders believed the cancer was a result of her experience in 2001. "I definitely believe it because I haven`t had any illnesses," she told US newspaper the New Jersey Journal. "I don`t have high blood pressure ... high cholesterol, diabetes."
Thousands of people who were at Ground Zero that day have been since diagnosed with cancer, but medical officials have not confirmed any link to the attacks.
In 2011, Barack Obama instituted a $2.78bn (£1.77bn) fund to compensate first responders for health problems related to the attacks.
Ms Borders` daughter Noelle told the New York Post on Wednesday her mother "fought an amazing battle".
"Not only is she the `Dust Lady` but she is my hero and she will forever live through me," she said.
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