Of the many things I collect, there are many things that I have that fall into the "rare but no known value/no market" category.
For cards it would be a 1895 triple folder tobacco card that I had bought for $1 at a rummage sale, and then sent to SGC for grading. It was so rare that I could not actually find what set it belonged to. It was identified by the people at the old network54 non-sports forum and those people had said that the only info was in the old catalogs that you had to have a subscription for. Once it was identified, mine was only the 2nd graded and potentially the 3rd known to exist. But there is no market and no sales history for that card so it has no actual value other than $19 (the price I paid plus cost to grade).
There are other things, such as the un-numbered proof or replacement cards from Pacific that came out of their bankruptcy auction. To this date I have yet to find any "duplicates" of the ones that I had acquired, especially not any of the 02-03 Pacific Nights SE which would be the easiest to identify.
TCDB Collection Leaderboard spots:
#1 Alexei Zhamnov #1 Shane Doan #1 Phoenix Coyotes #1 Arizona Coyotes