The morphology and dimension of the conductive filament formed in a memristive device are strongly influenced by the thickness of its switching medium layer. Aggressive scaling of this active layer thickness is critical toward reducing the operating current, voltage, and energy consumption in filamentary-type memristors. Previously, the thickness of this filament layer has been limited to above a few nanometers due to processing constraints, making it challenging to further suppress the on-state current and the switching voltage. Here, the formation of conductive filaments in a material medium with sub-nanometer thickness formed through the oxidation of atomically thin two-dimensional boron nitride is studied. The resulting memristive device exhibits sub-nanometer filamentary switching with sub-pA operation current and femtojoule per bit energy consumption. Furthermore, by confining the filament to the atomic scale, current switching characteristics are observed that are distinct from that in thicker medium due to the profoundly different atomic kinetics. The filament morphology in such an aggressively scaled memristive device is also theoretically explored. These ultralow energy devices are promising for realizing femtojoule and sub-femtojoule electronic computation, which can be attractive for applications in a wide range of electronics systems that desire ultralow power operation.