Auras will not fall off if something is made untargetable.

Aura spells do target when they are cast. The targeting restrictions are denoted by the object type that appears after the word ‘enchant’ in the text box. However, once in play and attached to a permanent they do not target what they are attached to. This means that making it so a permanent cannot be targeted will not do anything to the aura.

For example, if a creature were to have a Trollhide attached to it, equipping it with a Whispersilk Cloak will not cause the Trollhide to go to the graveyard. Similarly, if a creature you controlled is enchanted by an opponent’s Pacifism, equipping it with a Swiftfoot Boots will not do anything to the Pacifism.

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