This paper deals with a conceptual study on a plutonium (Pu) and minor actinide (MA) burning fast reactor core for the distant future phaseout of a fast reactor fuel cycle after it is commercialized and used for a long time. This burning core aims to reduce the Pu and MA inventories contained in the fuel cycle through multiple recycling. A key point for the core design is the degradation of Pu and MAs during multiple recycling. This degradation affects the feasibility of the nuclear design by increasing the sodium void reactivity and decreasing the absolute value of the Doppler constant. A feasible core concept was found by incorporating the following three factors to improve the reactivity coefficients: core geometry flattening, fuel burnup reduction, and use of silicon carbide (SiC) in the cladding and wrapper tubes. Notably, softening the neutron spectrum using the SiC structural material not only improved the reactivity coefficients but also indirectly mitigated the degradation of Pu and MAs. Consequently, the designed core allowed for multiple recycling to continue until the Pu and MAs reduced significantly, particularly by about 99% in a phaseout scenario starting from a fast reactor fleet of 30-GWe nuclear power capacity. Fast reactors were found to have the potential to become self-contained energy systems that can minimize the inventories of Pu they produced themselves, as well as long-lived MAs. Fast reactors can be among the important options for environmental burden reduction in the future.