It says, "Any Phase: Each opponent discards the top 2 cards from his or her deck for each character in his or her dead pile. (Limit 1 per round.)"

Can i play it if my opponent have no card in his dead pile?

Nope. You can't trigger an ability/play an event if its effect would not be expected to change the gamestate - for instance, you can't stand the newest Janos Slynt if you're draw-capped. This is encompassed in the FAQ, in section 3.6 and is infamously known as the Janos Slynt ruling.

So even though the keyword (prized) would change the board state, since the effect of the ability (any phase) wouuldn't, you can't play the event at all.

Let's say there was an event card that states "Discard one card from hand and return two characters from your dead pile to hand" And you only have one card in your dead pile.

By Istaril's example you *could* play the event because the game state has changed?

Yes.

In order to play an event (or use a triggered ability), at least one, independent part of the effect must do something when it resolves -- even if it doesn't do everything it possibly could do. So an effect that says "discard 2 cards," for example, could still be used if someone had only 1 card to discard -- because the effect would result in something happening.

So Heads on Pike is ok in a melee game if only one opponent has a dead pile but your other opponents have no dead people