Can elemental hero absolute zero destroy stardust dragon with its effect even though EHAZ it does not activate on the field?

Yes, Elemental HERO Absolute Zero's effect to destroy a monster can still be activated even if it is not on the field. This is because Absolute Zero's effect is a Trigger Effect, which means that it activates when a specific event occurs, regardless of where the card is located. In this case, the event that triggers Absolute Zero's effect is when another monster is destroyed by battle or by a card effect. Once this event occurs, Absolute Zero's effect will activate, even if it is in the Graveyard or banished.

When Absolute Zero's effect activates, you can target 1 monster on the field and destroy it. This effect does not target Absolute Zero itself, so Stardust Dragon's effect to negate and destroy targeting effects will not be able to stop it. Therefore, Absolute Zero can destroy Stardust Dragon with its effect, even if it is not on the field.