Edge MHD instabilities with pressure collapse are found in relatively high beta and low magnetic Reynolds number regions with a magnetic axis torus outward-shifted configuration of the large helical device (LHD), and characteristics and onset conditions of the instability are investigated. The instability has a radial structure with an odd parity around the resonant surface, which is different from that of the interchange instability typically observed in the LHD. The onset condition dependence on the magnetic axis location shows that the onset beta increases as the magnetic axis location moves more torus inwardly, and the instability appears only in limited configurations where the magnetic axis is located between 3.65 and 3.775 m. In such configurations, the resonant surface location is close to an index of the plasma boundary. This fact suggests that the distance between the resonant surface location and the plasma boundary plays an important role in the onset, and a possibility that the instability is driven by an external mode.