Mechanism behind negative conductance of ion channels
This is the figure OP talks about:



Negative Conductance Caused by Entry of Sodium and Cesium Ions into the Potassium Channels of Squid Axons, Francisco Bezanill, Clay M. Armstrong (1972).

Short answer is that in non-linear mode of ion channel operation other ions start passing through it (channel loses specificity). Cumulative effect (because of different concentrations of different ions) is negative total conductance, if you don't measure currents of specific ions.