The classical Hertzian contact model establishes a monotonic correlation between contact force and area. Here, we showed that the interplay between local friction and structural instability can deliberately lead to unconventional contact behavior when a soft elastic shell comes into contact with a flat surface. The deviation from Hertzian solution first arises from bending within the contact area, followed by the second transition induced by buckling, resulting in a notable decrease in the contact area despite increased contact force. Additionally, our results invalidated a previous claim of a linear relation between friction and dissipated energy, demonstrating the suppression of both buckling and dissipation at high friction levels. Different contact regimes are discussed in terms of rolling and sliding mechanisms, providing insights for tailoring contact behaviors in soft shells.