It has been established that the sources contributing to the cosmic X-ray background (CXB) emission are mainly nearby active galactic nuclei (AGNs), in particular those that are obscured. Thus, it is important to fully identify the hard X-ray sky source population to accurately characterize the individual contribution of different AGNs to the overall CXB emission. We present a follow-up analysis of all 218 sources marked as unidentified in our previous revision of the third release of the Palermo Swift -BAT hard X-ray catalog (3PBC) based on our multifrequency classification scheme. These 218 sources were classified as unidentified in our previous analyses because they lacked an assigned low-energy counterpart. We searched for soft X-ray counterparts of these 218 3PBC sources in archival Swift -XRT observations obtained between January 1, 2005, and August 1, 2018. In particular, we found 1213 archival Swift -XRT observations for 192 of the 218 unidentified sources. We find 93 possible Swift -XRT counterparts within the Swift -BAT positional uncertainty regions. They correspond to 73 3PBC sources, 60 of which have only a single Swift -XRT detection; the rest have multiple detections. We present all the detected possible counterparts of the as-of-yet-unidentified hard X-ray sources to the community as a catalog for future spectroscopic follow-up targets, together with a short catalog of our classification of the ten sources for which there were available spectra.