Aegis Angel has an enters the battlefield ability that will make another targeted permanent indestructible for as long as the Angel remains in play. Indestructible means that this permanent will not be destroyed by effects that say to destroy or if it is a creature by receiving lethal damage.

In most cases, what happens is pretty simple; as long as the Angel is in play the permanent that is affected by the Angel’s ability will not be destroyed. However some effects will destroy or deal lethal damage to the Angel at the same time as this other permanent. What happens to the protected permanent depends on the effect.

For example, if the Angel is making a Runeclaw Bear Indestructible and a Day of Judgment resolves, only the Angel will be destroyed. This is because when the one-shot effect from Day of Judgment is applied, the Bear is indestructible.

However, if both this Angel and protected are in play and both targeted by Chandra, the Firebrand‘s ‘ultimate’ ability both will end up being destroyed, just not quite at the same time. After Chandra’s ability resolves, state-based actions are checked and the Angel will go to the graveyard as it has received lethal damage. Then after state-based actions are applied, they are checked again. At this point the Bear will have received lethal damage, and because the Angel is no longer in play it will not be indestructible. Because of this it will then go to the graveyard.