Oh my. Surely somebody has said it already, but I just realized: Possession+Donate is going to be so degenerate.
It shouldn't be a problem. Donate takes place after your turn, so if the Possessor has the Possessed player buy Donate, the Possessed player gets to decide what to trash.
Will it be a problem if I donate and trash my deck down to village-village-possession-possession-possession?
Yeah... so I am pretty swayed toward the degenerate case here actually. When you can reach a deck that plays more than 1 Possession a turn without falling super far behind, the goal turns into building this up as quickly as possible and then destroying your own economy. You can destroy your own economy instantly with Donate, and leave your deck in debt so your opponent can't use it. If this is mirrored, the game is locked out and you starve to death.
Also... FTFY:
Will it be a problem if I donate and trash my deck down to king's court-king's court-possession-possession-possession?
I've thought a bit more about this:
Stalling and Donating all the money is strictly worse than stalling and donating everything but a copper. Your opponent can't do anything with your deck anyway, except buy coppers and curses (and poor houses and Debt stuff), which they would do anyway with their own deck if they kept a copper.
If you are ahead by more than 4-8 points, keeping a Silver's worth probably makes you win. (you
slowly win by three-piling and Donating Curses, Coppers and Estates, or three 2-4$ cards as long as the extra economy needed doesn't give your opponent access to more points than just the Estate pile). If you don't have that point advantage, your opponent will probably use your not-completely-dead deck to gain more points than you do and you'll lose, so it's in your best interest to starve to death (nobody likes losing).
Supposing that the players are playing to win, and supposing that starving to death counts at best as a draw, it would be in their interest not to build a stall-inducing Possession deck unless they are going to win after most Estates go to their opponent.
So, I don't see the stall happening a lot of the time. You don't often have both a point lead and the time to buy Possessions while defending that lead.
(the long and drawn-out endgame of such a scenario might offer some small chances for the losing player to build up a sloggish deck with coppers silvers and Estates and lucksnipe a couple of Duchies while their opponent does not. Thus, they unfortunately might not want to resign right away)