Recent progress is nanoscale photonics is driven by the physics of Mie resonances of high-index dielectric nanoparticles that provides a novel platform for localization of light in subwavelength photonic structures and opens new horizons for metamaterial-enabled photonics, or metaphotonics. We introduce a novel physical mechanism for achieving giant quality-factors (Q-factors) in finite-length periodic arrays of subwavelength optical resonators. The underlying physics is based on resonant coupling between the band-edge mode and another standing mode in the array and the formation of localized states with dramatically suppressed radiative losses.