Giacoma (Genevieve) Biundo was born around 1878 in Cinisi to Salvatore Biundo and Caterina (Rosalia) Ferrante.

(Even though she was just a little younger than him, she was the niece of Giuseppe Biundo who immigrated to New Orleans, as her father, Salvatore Biundo, was his older brother.
And though she was much older than him, she would have been first cousin to Joe Biundo. Her children were closer to his age.)
She married Salvatore (Sam) Randazzo sometime before 1908. The first record we have is of her with her children immigrating in to join her husband in the United States.
Immigration
She and her children had initially been scheduled for passage in November of 1915; however, they hadn’t made that one for some reason as their names were crossed out on the passenger record with no further details or markings. That may have been when her father, Salvatore Biundo died, as her mother, Caterina Rosalia Ferrante, came to Chicago shortly after she did and was listed as widow.
They had been scheduled again in February 1916, with her name and all her children’s names listed again, but they hadn’t made that one either. (When the passenger record shows a line through the person’s name and all the way across, with no further markings and no details added about where they were going, etc, it shows that person did not make that voyage.)
They finally did arrive in the United States around November of 1916. Below is a record of Detained Aliens on November 3rd, 1916 in New York which includes Biundo, Giacoma and her 5 children. The cause of detention was that she had to wait for money from her husband to arrive to pay for train travel. He was already living in Chicago, and when the money arrived, they could go join him.

Chicago
On October 5th, 1917, her mother, Caterina Ferrante (age 62), arrived in New York. Her passenger record stated that she was going to stay with her daughter, Giacoma Biundo, who was living in Chicago.
Salvatore Biundo had died by that time because Caterina is listed as widow. (Caterina’s last name was Ferrante even though her husband was Salvatore Biundo because women retained their maiden names in Italy.)
Traveling with Caterina Ferrante was another daughter, Maria Biundo (age 27).
I don’t know if Caterina Ferrante and daughter Maria Biundo stayed, moved elsewhere, or if they were just visiting and returned to Sicily afterward because I haven’t seen any further records on them. They were not with the daughter Giacoma (Genevieve) on the 1920 census.
According to the 1920 census record, Giacoma (now listed as Genevieve) was 43 years old, living in Chicago with her husband (Sam, age 49) and with their children (Rose age 12, Frank age 9, Mary age 8, Joseph age 6, and Cecilia age 1 and a half).
They lived at 509 South State Street in Chicago. Also living there at the same address was her younger sister, Rose (age 35), along with her husband Ciro Palazzalo, and their daughter, Genevieve (age 4 months?).
It confirms that Giacoma (Genevieve) had immigrated (with the children) in 1916, and her husband Sam had immigrated in 1915. (Her sister, Rose, had immigrated in 1917.)

Children of Giacoma Genevieve Biundo and Salvatore Randazzo:
Maria Grazia Randazzo (1901) married Salvatore Maniaci
Rosalia “Rose” Randazzo (1908) married ? Cusimano
Faro “Frank” Randazzo (1910)
Anna (Mary) Randazzo (1912)
Giuseppe “Joseph” Randazzo (1914)
Cecilia Randazzo (1918)