One problem with questions about the ordinary people is we don't know that much, at least by the time period (three kingdoms) I'm familiar with. The histories were focused on the courts and the Emperor, of important people of the gentry class (like the writer would have been), a lot of things escape through the fogs of history. Works that get lost, Han rituals as there was an assumption it was known and rarely got noted down, the lives of the farmers were not the focus of writings.

When we do come across farmer found something (examples Wang Ding finding jade seal, some in Hanzhong, Wang Xiu and Zhang Jia) we rarely found out what happened to said seals. Wang Xiu and Zhang Jia supposedly gave it to Guan Yu from the memorial Shu officers sent up to Liu Bei to urge him to become Emperor but the other two, simply the discovery is mentioned. In each occasion it was used to justify potential regime changes and the use of such omens of convenient items being found should perhaps be taken with a pinch of salt. There was a case in 279 where tomb raiders found ancient texts and that was stored in the Jin imperial archives but that was a crime rather then found so easy for Jin officials to take.

In terms of governments, they did often seek to rebuild book collections and restore archives if there had been a time of chaos that had left the archives diminished or near destroyed. However details on how, bar having their historians and scholars writing up the texts, they rebuilt the archives isn't clear. The first payments I'm aware of where the court paid (via a roll of silk) for private collections was Emperor Wen around 582

Sources:

Rafe De Crespigny A Biographical Dictionary of Later Han to the Three Kingdoms

Anthony Bruce Fairbank Ssu-ma I (179-251): Wei Statesman and Chin Founder, an Historiographical Inquiry

Most central government in imperial China adopted policy that encourage people to transfer antiquity to authority. In Sui, Tang, Ming, Qing dynasty, many emperors tried to collect ancient scrolls, classics. The story of the discover of "Bamboo Annuals" is a typical case to observe the attitude of imperial governments. "Bamboo Annuals" is an early chronicles of ancient history, it mentioned historical events which start from 2000BC to 300BC. In Western Jin Dynasty(279AD), someone tried to rob a tomb of an ancient warlord. While the thief had been caught by the officials, the government discovered a number of written records in the tomb. After the discovery, Emperor Jin Wudi assembled all important scholar officials to decipher and arrange them. Since the central government really value antiquarian books, some people tried to give fake books to bureaucrats and scholars. The discovery of "Book of history in Old Language(fake)" in Eastern Jin dynasty is one of the most well-known example.

There were cases that people sold antiquity after they found it. Sometimes because peasants did not know that thing was an antiquity. For instance, oracle bone inscriptions were considered as drug ingredients for a long period. Until it bought by scholars in Qing Dyansty, people realized the value of these oracles.

So if we live in imperial China, hand in your antiquity to government bureaucrats or scholars is a good choice to obtain fame and wealth.

Sources:

"隋書"(History of Sui)，中華書局，1997年9月

董洪利主編: "古典文獻學基礎"，北京大學出版社，2008年7月