Energy transfer is an essential light-matter interaction. The transfer efficiency is critical for various applications such as light-emitting, optical modulation, and the photoelectric effect. Two primary forms of light-matter energy transfer, including absorption and emission, can be enhanced in optical cavities. Both forms can reach an extremum inside the cavity according to the coupled-mode theory. Graphene conductivity at the terahertz frequency can be tuned from positive to negative, providing a suitable material to study switchable extremums of these two forms. We integrate graphene with a nested cavity where an infrared cavity is inserted in a terahertz cavity, thereby achieving terahertz perfect absorption at the static state and optimal gain under photoexcitation. Leveraging an inserted infrared cavity, we can elevate the working efficiency by strongly absorbing the infrared pump. We also numerically show the feasibility of electrically tunable extreme energy transfer. Our concept of the nested cavity can be extended to different materials and even to guided modes. A switchable synergy of loss and gain potentially enables high-contrast dynamic modulation and photonic devices with multiplexing functions.