If an effect prevents a piece from being damaged or destroyed, does that also prevent the piece from being removed or replaced?

If an effect prevents a piece from being damaged or destroyed, does that also prevent the piece from being removed or replaced?

• "Stubborn Solidity," a Unique Power of Stone's Unyielding Defiance, prevents Dahan from being changed in any way.
• "Fortify Heart and Hearth," a Special Rule of Hearth-Vigil, explicitly prevents Dahan from being destroyed or replaced by Events. (It doesn't prevent them from being removed, but no such Events exist as of the release of Nature Incarnate.)
• "Thwarting the Sneaky Thieves," a rule in the Despicable Theft scenario, explicitly prevents Thieves from being destroyed, removed, or replaced in certain circumstances.