In the early days of the Cultural Revolution, Deng Xiaoping and Liu Shaoqi were criticized for following the "bourgeois reactionary line" because they sent working groups to suppress the more Mao-leaning "rebel groups". At the Eleventh Plenary Session of the Eighth Chinese Communist Party (CCP) Central Committee held in August 1966, Mao Zedong retook the first-line leadership. Liu and Deng were criticized by Lin Biao and others in the party, leading to their power declining; Liu and Deng thus stopped participating in Central Committee leadership duties. As the Cultural Revolution became more and more intense, Deng was unable to escape large-scale criticism, and no longer appeared in public. He was placed under house arrest at his home in the Zhongnanhai (the seat of CCP power).
However, Mao had long made a clear distinction between Liu and Deng. Deng was well-versed in Mao's thinking; Deng repeatedly reflected on his mistakes, and promised that he would "never try to rewrite the history books" and "would never be an unrepentant capitalist roader", in hopes that the Central Committee would give him a chance to make a fresh start.
In the top CCP ranks, Lin Biao became Mao Zedong's appointed successor; but within a few years of this, a rift developed between Lin and Mao. During the Central Committee's Ninth National Congress in April 1969, Lin Biao and Chen Boda opposed continuing the Cultural Revolution and advocated for focusing on developing productivity. Mao rejected this; and his rejection became the key turning point in the relationship between the two sides. At the Lushan Conference in 1970, Lin Biao's clique fell into a power struggle with "Gang of Four" member Zhang Chunqiao and others. This angered Mao Zedong; Mao and Lin formally ceased contact.
In 1971, Lin Biao attempted to flee, but died in a plane crash. This was a turning point in Deng Xiaoping's life. On November 8, Deng Xiaoping sent a letter to Mao Zedong, expressing his loyalty and asking Mao to arrange a job for him, but received no response. On August 3, 1972, Deng again wrote a long letter to Mao Zedong, in which he criticized the Lin Biao clique for treason to the Party and the country; Deng emphasized that he would "never try to rewrite" his own past mistakes, and that he was still determined to contribute to the Party and to the people to compensate for his past mistakes.
On August 14, 1972, Mao Zedong gave comments and directives regarding the letter. Mao said that Deng should be treated differently from Liu Shaoqi, and praised Deng for his sincerity and military accomplishments, both before and after the CCP's founding of the People's Republic. On March 10, 1973, the CCP Central Committee published the "Decision on Restoring Comrade Deng Xiaoping's Organizational Life in the Party and Post as State Council Vice Premier"; this Decision was issued to the entire Party, marking the official comeback of Deng Xiaoping.
References: Yang Jisheng, "The World Turned Upside Down: A History of the Chinese Cultural Revolution"