Here's my current submission (this card has been updated):
A couple of notes
1) The setting aside happens in the same way as possesion; you don't get the card back until after cleanup, meaning you will not be able to draw them.
2) The setting aside happens on all turns including your opponents (or between turns for donate), but putting it into your discard pile (or trash) happens at the end of your turn only.
3) This will work if you trash cards on your opponents turn via knights, swindler, saboteur, bishop, etc. (as far as who counts as the trashers owner; follow the already established rules).
4) Each player has their own set aside area; this is not one communal pool. In other words, your not gaining cards you're opponent trashed.
5) This can be used to get trash for benefit without actually trashing.
6) This excludes cards trashed from the supply,or else salt the earth can become way too crazy sometimes.
7) Taking a cue from Aquila, I made this an edict.
Updates:
1) This now happens after you trash rather than when you trash. thus any "when you trash" abilities happen before this. If the card is no longer in the trash Regret has lost track of it. This was mainly to make it so someone couldn't posses you and then trash your cards (choosing to use Regret's ability first), set them aside, and then put the good ones in the trash. As a result, you now cannot set aside your fortress with this.
2) changed "not from the supply" to other than from the supply" to more clearly indicate trashing a card directly from the supply.
3) You now put your cards back at the end of every turn (including other player's). This is to make it a little less swingy. it used to be if your opponent knights you twice, then on your turn if you play a steward, you get to trash 2 cards (instead of what would be effectively 1 in a game like this) and get your 2 cards back. Now, if your opponent knights you twice, you trash 1 and keep 1. You obviously don't have control over what happens on your opponents turns so I think this is better. Technically cards trashed from donate will get put back at the end of your next opponent's turn.