If a character has Head of a Dwarf attached and somehow loses Infamy (from King Balon's Host, for instance), what happens when the character's controller would claim power for his or her House?

1. the power goes to the character anyway
2. the power goes to the House card
3. the power doesn't go anywhere

It would go on a character with Head of a Dwarf anyway. The trick, of course, is that you only do it when you claim power (as stated in the second part of the attachment's effect), and not when you move power to your House. Losing the Infamy means you don't have an option, on that card anyway, of moving the power to the character instead of your House card.

Compare the situation to the Brotherhood Agenda (requiring the placement of the power on a character without granting Infamy).

Thanks for the answer. The comparison with the Brotherhood Agenda makes it clear.