Narrow Fe-K$\alpha$ Reverberation Mapping Unveils the Deactivated Broad-Line Region in a Changing-Look Active Galactic Nucleus

"Changing-look active galactic nuclei" (CLAGNs) are known to change their apparent types between types 1 and 2, usually accompanied by a drastic change in their luminosity on timescales of years. However, it is still unclear whether materials in broad-line regions (BLRs) in CLAGNs appear and disappear during the type-transition or remain at the same location while the line production is simply activated or deactivated. Here we present our X-ray-optical monitoring results of a CLAGN, NGC 3516, by Suzaku, Swift, and ground telescopes, with our primary focus on the narrow Fe-K$\alpha$ emission line, which is an effective probe of the BLR materials. We detected significant variations of the narrow Fe-K$\alpha$ line on a timescale of tens of days during the type-2 (faint) phase in 2013-2014, and conducted "narrow Fe-K$\alpha$ reverberation mapping," comparing its flux variation with those of the X-ray continuum from a corona and $B$-band continuum from an accretion disk. We derived, as a result, a time lag of $10.1^{+5.8}_{-5.6}$ days ($1\sigma$ errors) for the Fe-K$\alpha$ line behind the continuum, which is consistent with the location of the BLR determined in optical spectroscopic reverberation mapping during the type-1 (bright) phase. This finding shows that the BLR materials remained at the same location without emitting optical broad-lines during the type-2 phase. Considering the drastic decrease of the radiation during the type-transition, our result is possibly inconsistent with the hotly-discussed formation models of the BLR which propose that the radiative pressure from an accretion disk should be the main driving force.