Few things in Dominion are irreversible these days. People have even figured out ways to
put split piles back in arbitrary orders!
However, one element of Dominion has always had more of a sense of finality to it: the trash. Once something is trashed, it's gone forever, right? That's at least how we explain the game to our friends -- discarding means you'll see it again, trash means you won't.
Of course, that's changed over the expansions, starting with Dark Ages. (Technically, Thief / Noble Brigand took treasures they stole out of the trash, but since they were only in the trash for a brief moment in the midst of resolving the card, we won't count that. I also won't count Fortress for the same reason.) Dark Ages introduced us to Graverobber and Rogue, which can all take cards of a specific price range ($3-$6) out of the trash. Of course, which cost reduction like Bridge and Highway, this meant that any cards costing $3-$11 (i.e. $3+ with no potions) could be retrieved from the trash.
Lurker provided the next big jump up: Now any action cards could be taken from the trash, including cheap ones (e.g. Ruins) and potion-cost ones.
And now finally, Treasurer has given us a way to get any Treasure out of the trash. Of course, this is the biggest deal for heirlooms like Magic Lamp and Haunted Mirror, which no longer are just single-use. But it's also now the first time we can take Coppers out of the trash!
This leaves us with only a small number of cards that cannot be taken out of the trash once they make it there. Here they are: