Also can happen in games with Ambassador. By the end of my last game with Lord Rat--with Ambassador in Kingdom--Rat had in its hand: 1 Prov, 1 Dutchy, 1 Duke, and 1 Ambassador...having given tons of free silver and several valuable action cards to me over the course of the game.
These types of games are funny to look at, but not at all enjoyable to play, of course. I guess Apprentice and Ambassador are especially difficult to code for.