If a nonmodal double-faced card has somehow become a copy of Enduring Angel, the replacement effect will apply, the copy of Enduring Angel will transform, and your life total will become 3. However, because the copy effect that makes it Enduring Angel continues to apply to it after it transforms, it will still be a copy of Enduiring Angel. This means that the replacement effect will be applied again if your life total would be reduced to 0 or less a second time while that copy effect is still applied.

Applying the replacement effect can't cause Enduring Angel to transform if it isn't a double-faced permanent; that is, if it's a token or if a single-faced permanent has become a copy of it. In that situation, you will lose the game.

Enduring Angel's last ability is a replacement effect. It doesn't use the stack and can't be responded to. Notably, players cannot try to destroy Enduring Angel to prevent it from transforming and cause you to lose the game.