In the series, the Archivists do collect and preserve cultural heritage (in this case what are essentially copies of burned books, etc), it is so that they are able to sell what they have on the black market. They exist on the fringes of society (the only reliable way to find one is to go to the museum, go to the patriotic exhibit, and ask to hear about "the glorious history of [the providence]") and they trade in information and connections as well.
The first mention of the Archivists in the series:
"There are people who call themselves Archivists," Ky says. "Back when the Hundred Committees made their selections, the Archivists knew the works that didn't get selected would be a commodity. So they saved some of them. [...]
"Cassia, the Archivists aren't altruistic. They saw a commodity and they did what they could to preserve it. Anyone can have it who's willing to pay, but their prices are high." (Matched, chapter 25, listened to audio version so I don't have a page number and the quote above may not be exact)