The Qin dynasty ended shortly after Qin's death, and was replaced by the Han dynasty. In A.D. 9, Wang Mang (45 BC - A.D. 23) usurped the throne from the ruling family and set up his own short-lived dynasty. During Wang Mang's reign, it was alleged that some of Confucius' writings had been rediscovered. Wang Mang apparently used these texts in an attempt to support his own reforms.
Robert Greene (in "The 48 Laws of Power," p. 397) explains it this way:
Reigning from A.D. 8 to A.D. 23, the Chinese emperor Wang Mang emerged from a period of great historical turbulence in which the people yearned for order, an order represented for them by Confucius. Some two hundred years earlier, however, Emperor Ch'in had ordered the writings of Confucius burned. A few years later, word had spread that certain texts had miraculously survived, hidden under the scholar's house. These texts may not have been genuine, but they gave Wang his opportunity: He first confiscated them, then had his scribes insert passages into them that seemed to support the changes he had been imposing on the country. When he released the texts, it seemed that Confucius sanctioned Wang's reforms, and the people felt comforted and accepted them more easily.
Burning Books, by Matthew Fishburn similarly reports:
The first recorded state-sponsored book burning is the destruction ordered by Grand Councillor Li Ssu in Ch’in China in 213 BC. The country had been newly unified under Ch’in Shih-huang-ti, and he signified his rule with the order to burn the books of any historian or partisan of the defeated Shih or Shu. The Emperor is also known for beginning construction of the Great Wall, and even forced people convicted of protecting books to work on its construction; condemning, as Borges incisively commented, ‘those who adored the past to a work as vast as the past, as stupid and as useless’. This was not, as Lois Mai Chan has emphasized, unmediated destruction. There were exemptions for all manner of practical or scientific works and, just as importantly, even the objectionable books were preserved in imperial archives and allowed to be kept by the official scholars. As is often the case with such suppression, it is difficult to assess the extent of the initial destruction, but it is certain that this centralization of the written record increased the devastation when the Imperial Archives were attacked and destroyed in 206 BC. The association between censorship and aridity has its symbol in the legend that grass never grew on the spot where the books of the scholars were burned.(p. 2)
While there is controversy (apparently to this day) about the nature and extent of Qin's burning of books, and of Wang Mang's (or others') possible editing or forging of Confucian writings, these controversies were all made possible by the fact that Qin had control of the geographic area where Confucius' works circulated, and the means for effectively destroying those works.
This parallels the history of the transmission of the Qur'an. The first caliph of Islam, Abu Bakr, is said to have collected the Qur'an in A.D. 634. Nevertheless, various versions of the Qur'an were apparently circulating during reign of the third caliph, Uthman (reigned A.D. 644 - 656). Uthman created a standard text of the Qur'an and had the other copies burned. This was possible because Uthman had control of the geographic area where the Qur'an circulated and the means for effectively destroying competing copies.
There is, however, no close parallel in Christianity. Christianity rapidly spread copies of books of the Bible (both Old and New Testaments) beyond the reach of the Roman Empire. Christianity had no centralized earthly ruler and by the time emperors like Constantine or Roman bishops tried to operate in such a capacity, the text of the New Testament was so well established and widespread that any attempt to edit or control the text would have been ineffective. While this uncontrolled transmission of the text may seem messy it is one of the means by which we can have confidence in the text today, without the need for a continued prophetic witness.
P.S. For your interest:
There is considerable debate about which, if any, of these books were directly written by Confucius himself. The main source of his quotations, the Analects, was not written by him. As with many other spiritual leaders such as Siddhartha Gautama, Jesus, or Socrates, our main source of Confucius' thought, the Analects, was written down by his disciples. Some of the core canon is argued to have been written by Confucius himself, such as the Spring and Autumn Annals. There is considerable debate about this, however.(source)
This factor is further complicated by the "Burning of the Books and Burying of the Scholars", a massive suppression of dissenting thought during the Qin Dynasty, more than two centuries after Confucius' death. The emperor Qin Shi Huang destroyed a great number of books, possibly destroying other books written by Confucius or his disciples in the process.
The current canon of Four Books and Five Classics was formulated by Zhu Xi. Many versions contain his extensive commentaries on the books. The fact that his specific version of the Confucian canon became the core canon can be seen as an example of his influence in Confucianism.
Other books are not included in the current canon but once were. The major example is the Xun Zi.
In AD 9, Wang Mang usurped the throne and created the Xin Dynasty. The Western Han dynasty had ended after 198 years of consecutive rule.(source)
Wang Mang hoped to gather support from the peasantry be introducing reforms. Wang Mang announced the discovery of books written by Confucius, which were supposedly discovered after Confucius’ house, was destroyed more than two hundred years ago. The discovered work supported the same kind of reform that Wang Mang sought.
Wang Mang defended his policies by quoting from the discovered books. Following what was portrayed as Confucian scripture; he decreed a return to the golden times when every man had his measure of land to till, land that in principle belonged to the state. He declared that a family of less than eight that had more than fifteen acres was obligated to distribute the excess amount of land to those who had none.