The power Living Shadow (Demon: The Descent 169) is silent on whether it crosses realms. My storteller usually doesn't let us take powers across certain realms (such as the Hedge), but is there a rule that says this power can't be used to follow someone into Shadow or the Underworld as long as shadows are cast there?
Is there a general rule in any book (Chronicles of Darkness, Mage, etc.) about any similar buffs like mage armor ending when the subject transitions to a new realm?
You point out that the DtD manual is silent on the matter. However there are some clues. First, none of the gateway manifestations (Shadow Gate, Underworld Gate, Avernian Gateway) have a "passenger limit". By that I mean that the invoker does not have to pay an additional cost per person brought through the gate. Shadow gate specifically says that even people wandering by can go through the gate. So in CoD it seems that gate spells create a physical portal that (after they are created) not require anything from those who cross it.
Then as written, anyone can follow someone who is passing through a gate as long as the gate is open. If a PC were invisible they could tag along, or if they were miniaturized they could perhaps hide in the pocket of someone passing through. Living Shadow is a similar case in which a demon can accompany someone undetectably as they walk, so long as they cast a shadow.
Of course some realms might not have clear shadows, and the demon using the power has no guarantee that they can return to the physical plane if the gate closes. If I were the ST I would remind the PC that they don't know how shadows work in other realms and so things might not go the way they expect.
