The card must be present in the ash heap to be redrawn.

If the card is cancelled, the self-replacing clause is also cancelled.

If an effect delays when the redraw occurs (e.g. The Meddling of Semsith), you can still redraw this card from the ash heap when the delay effect allows a redraw.

If an effect prevents replacement (Visit from the Capuchin), then there is no opportunity to use the cards replacement text.