What happens if you ambassador a hovel?

Question

In Dominion, what happens when you Ambassador (Seaside) a Hovel (Dark Ages)?

Answer 1

Nothing happens at all.

There's a (likely unofficial) rules clarification on Ambassador's Dominion Strategy wiki:

If you reveal a card which is not in the Supply, such as Spoils, Madman, Mercenary, or Shelters, Ambassador does nothing.

The same article also quotes an official FAQ clarification:

If the pile for the chosen card runs out, some players may not get one; cards are given out in turn order starting with the next player.

Since Hovels are not present in the Supply, you cannot return your hovels there. Further, nobody can gain them: since they aren't available in the Supply, they are effectively perpetually out of stock.