Israel, son of Yosef Baruch and Raizel Shoshana, was born in 1928, in Cologne, Germany, to a Haredi rabbinical family. In the family, there were ten siblings.
When Hitler rose to power, the family moved back to Poland, where they had come form. When they got certificates, they made aliyah and settled in Tel Aviv. The family had difficulty finding a place to live, but the mother was resourceful. The family kept up a Haredi life. The father worked at different jobs in order to support the family and allow his sons to continue studying in yeshiva. When the Port of Tel Aviv opened, he opened a cafeteria there, which he ran until the port closed. The cafeteria became a meeting-place for everyone who came to the port as well as all manner of influential people and veteran citizens.
Israel studied in the yeshiva in Pardes Hannah, where he was hosted by the Freund family. Upon his return to Tel Aviv, he studied at Yeshivat Tel Aviv. Israel was a good student, known for his academic prowess, his sense of humor and his pleasant demeanor. He loved to joke around, as well as hiking and picnicking, where he was always in good spirits. In yeshiva, he was recruited by Lehi. Two brothers were in the Hagana, while one was in the IZL. In his family, there was no political consensus, and so they did not discuss these topics. Israel was a sports fan, very active in Young Maccabee, on the Moledet team. Israel was captured by the British when he was putting up posters, and he was sent to Latrun. In the camp, he organized morning calisthenics for the prisoners. Once he was released, he returned to his activities in sports and politics.
He started training Lehi youth in Raanana. Once the State was established, he joined the IDF at Sheikh Munis with his Lehi comrades. He was assigned to Battalion 88, the heavy mortar unit, of the 8th Brigade. He was the mortar sergeant during the battles in the Negev.
Two weeks before his death, he asked for a short leave so he could visit a friend of his who had been wounded and hospitalized. Israel fell during Operation Horeb against the Egyptians, on December 29,1948 the third day of Hanukkah, a few days before his birthday on the Hebrew calendar. He was buried in Rehovot on December 31,1948. One of his eulogizers told how Israel had volunteered to stay at this post in place of a family member so that the latter could stay longer at home.
The Pivco family lost another son, Aharon Eliezer, a Hagana member, who was 24 when he died.
In 1952, Young Maccabee held a memorial evening, and the Moledet team was renamed in his honor. They also published a memorial album.