If this card is destroyed while face-down, it still does damage to your opponent.
If this card’s activation is negated, such as with "Magic Jammer" or "Riryoku Field" it does not do damage to your opponent.
"Black Pendant" activates in the Graveyard, so if it is destroyed when "Imperial Order" is on the field, it still does damage to your opponent.
You can chain to the activation of the effect of "Black Pendant" when it is sent to the Graveyard.