Sawyer suffered a heart attack and later died on January 21 at the Motion Picture Television Fund retirement home where she resided, according to Dudley.
The character actress appeared in multiple film and television projects over the years, including roles in "Archie Bunker's Place," "Will & Grace" and "When Harry Met Sally." More recently, she appeared as the mother of James Woods's character in the Showtime series "Ray Donovan."
"I loved working on 'Donovan' -- my son was a hit man, and I really got to cuss," she told The Hollywood Reporter in 2015.
Sawyer was born Rosie Cohen in Pueblo, Colorado, in 1912 (the same year the Titanic sank) to a Jewish family from Romania.
Her parents, Samuel and Dora Cohen, moved to Oakland when Sawyer was young and she enrolled in dance lessons.
Her mother's love of theater and vaudeville led Sawyer toward acting as an 8-year-old. As a teen, she won amateur contests and landed her first professional gig on the radio.
From there, Sawyer started doing a comedy act, performing on the Vaudeville circuit and nightclubs.
"I learned all about show business," she told People last year.
"I played every nightclub across the United States in the '30s, and some of them were real dumps. But that's how I got into the biz."
Sawyer was briefly married to Marshall Schacker and gave birth to two daughters as she continued to build her acting career.
Her daughter told CNN that family was very important to her mother.
"She was a loving mother to us and had a large extended family that she always kept in contact with," Dudley said. "She had four grandchildren and three great-grandchildren upon her death. She leaves us and a large extended family."
Sawyer also built a family in the industry she loved.
Her big break came in 1957, after Lillian Small, an agent for Frank Sinatra, caught her performance as a tipsy society lady in the Broadway comedy "A Hole in the Head."
The singer purchased the rights for the play, and Sawyer was the only Broadway cast member hired for the film.
That led to roles alongside Jackie Gleason, Kirk Douglas, Milton Berle, Robert Mitchum, Susan Hayward and Dean Martin.
She never stopped working, and Sawyer said she was perfectly happy not becoming a major star.
"On the whole, it's been a good [career] considering I began in nightclub dumps," she told The Spectrum in 2016.
"Frankie (Sinatra) told me 'Never give up and you'll always find a good part somewhere, sometime.' And I did."
Dudley self-published her mother's memoir, "I Never Wanted to Be a Star -- And I Wasn't," last year.