We discuss the results obtained so far in our ongoing search for the $^6$Li isotope in very metal-poor halo stars through very high resolution and S/N spectroscopy with the Subaru High Dispersion Spectrograph, and the consequent implications. Besides definitively confirming the existence of $^6$Li in the star HD 84937, we achieve a tentative detection in the extremely metal-poor star G 64-12 ([Fe/H]$\,{\simeq}\,{-}$3.2). For two other stars with [Fe/H] ${\sim}\,{-}3$, only upper limits were derived. Together with the VLT/UVES results of Asplund et al., this indicates unexpectedly high $^6$Li abundances in at least some stars at very low [Fe/H]. The findings are discussed in light of different production scenarios, including the structure formation cosmic ray model and other possibilities.