Back in the Dreamtime,when sabre-toothed Wombats roamed the Earth,& such firms as Mullard & STC made transistors,there was actually such a thing as a BJT which was reversible---It in fact was called a "Bipolar Transistor" to distinguish it from the common or garden varieties of BJTs that existed.
Just as an aside,"point contact" transistors were also reversible,if I remember correctly.
Yes,Virginia,there was such a thing as a "point contact " transistor!