Hazbiu was the son of Hazbi Cano Dautaj, a local leader during the Vlora War in 1920. He attended a commercial school and graduated from it in 1942. By that time he joined the Second World War from 1942 to 1944, affiliated with the communist and anti-fascist side of the National Liberation Movement.
After the founding of the People's Republic of Albania on 11 January 1946, he was elected Colonel Chief of Section of Counterintelligence in the Directorate for External Security. Later Hazbiu graduated from the Soviet Military Academy in Moscow.
In 1950, he was elected to the People's Assembly (Alb: Kuvendi Popullor) and was a member of it until October 15, 1982. He was also Deputy Minister of the Interior from 1950 to 1954, and at the 2nd Congress of the PPSh in April 1952 he succeeded as member of the Central Committee (Alb: Komiteti Qëndror) of the Party.
On 23 July 1954, he was the successor to Mehmet Shehu (who became prime minister) as the Minister of Interior. He held this post for almost 26 years, until April 26, 1980. He was also chief supervisor of the Secret Service Sigurimi, which was subordinate to the Ministry of the Interior. In 1957 he was promoted to Lieutenant General.
During the 4th Congress of PPSh in February 1961, Hazbiu became the candidate-member of the Politburo of the Party of Labour of Albania. In this capacity, he visited the People's Republic of China during the Cultural Revolution, in 1966 and 1968.
In November 1971, at the 6th Party Congress, he was elevated as a member of the Politburo. He remained within the supreme governing body of the PPSh until his resignation on October 13, 1982.
As Minister of the Interior during the mid-1970s, he was instrumental in the dismissal, arrest, and execution of the alleged conspirators of the military-economic spectrum such as Beqir Balluku, Petrit Dume, Hito Çako, Abdyl Këllezi, Koço Theodhosi, Kiço Ngjela, and Lipe Nashi.
On April 26, 1980, he became the successor of Mehmet Shehu, who remained Prime Minister, and finally Defense Minister while Feçor Shehu was appointed interior Minister of Interior. Hazbiu's appointment as Defense Minister was surprising, but followed a direct decision taken by the First Secretary of the PPSh Enver Hoxha, and F. Shehu's incapability to compare with major Defense Department Deputy Ministers' experience (Llambi Gegprifti, Nazar Berberi, Maliq Sadushi, or Veli Llakaj wanted to run for the post).
On October 15, 1982, Hazbiu was arrested and lost his membership in the People's Assembly and in the Politburo. On 23 November 1982, he was officially replaced by Prokop Murra as Minister of Defence, the first civilian to hold such a post of the People's Republic of Albania.
Shortly after Hazbiu's trial (and about a year after Mehmet Shehu's suicide on December 17, 1981) numerous other Party and State figures were arrested and convicted in 1983 in secret trials, including Shehu's wife Fiqret and his sons, former Interior Minister Feçor Shehu, who had long worked in management positions in the intelligence Sigurimi, most recently as its director, other senior intelligence officials, Foreign Minister Nesti Nase, and the Minister of Health Llambi Ziçishti. All were under Shehu's line on influence, and were accused of relations with the CIA, the Yugoslav UDB, and the KGB, allegedly having plotted a coup d'etat for the liquidation of Hoxha.
Incriminating statements were extracted under torture. Nevertheless, Hazbiu and Feçor Shehu could not be forced to admit the absurd accusations. Several defendants were executed, the others sentenced to long prison terms.
Kadriu was executed on September 15, 1983 in Linzë near Tirana. Twelve years after his death, his body was exhumed and buried at the family's request on 4 November 1995 in Selitë near Tirana.