(I probably ought to have a pat answer to this on the tip of my mind, but since I don't I'm going to wing it. This is probably just an opportunity to make an utter fool of myself. Please treat everything that follows with extreme suspicion.)
I think this is effectively an artefact of the model. That may not be true in the strictest sense -- it is possible such behaviour could be produced in real experimental preparations -- but it would require driving them in drastically non-physiological ways. I am not aware of this having been done, but I'm sure that's just my ignorance -- I would be surprised if nobody has tried.
In physiological terms, though: where would such a large constant current come from in a real cell? Where would the charges go? How would that be sustained with realistic boundary conditions?
While it is possible that such an effect can come into play very transiently in living systems, it seems unlikely that a true steady state of this kind could ever be reached.
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