According to the description of "What Actually Happens in a Harrowing" (WtO2E, p.184)
A Harrowing occurs when a wraith is dragged down by Oblivion for various reasons (see below) into the Labyrinth, there to become the temporary plaything of some Spectres working with her Shadow. As soon as one of the Harrowing conditions is met (endangerment of a Fetter or a Passion, etc.), a small Nihil opens directly underneath the character, and she descends at great speed through the Tempest.
Since the wraith is moving, as she would through the use of Argos, through the hyperspace of the Tempest, any goods she carries would be taken with her in the usual fashion into the Labyrinth. In the case of a Destruction Harrowing, I don't see any reason for the items to be left behind either, since the wraith reforms at a Fetter with one Corpus if they succeed. I'd imagine that a wraith who loses a Destruction harrowing has her goods lost in the Tempest, with the possibility of someone else finding them later at a random time.