I've used the polarity/steering capability of LEDs to make smart PS status indicators for each DC rail voltage in a console I did last century. I had a LED light Green for all good (PS at voltage up and fuse intact). LED Red indicated PS was up, but fuse was blown (open). And LEDs dark meant the PS was completely down or turned off.
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I've used a red LED once for a couple volt drop to generate a low current lower voltage alternate PS rail. I don't even recall exactly why I did this but did it inside a kit back in the 70/80s. I may have used one as a low voltage zener reference before but don't recall if that even made it into a production design.
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I don't recall LEDs specifying a reverse voltage breakdown but have used them in numerous multiplex applications where they tolerate modest reverse voltages without conducting or any ill effect. (some may specify a reverse current at some nominal voltage).
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Recently when I designed my crazy outlet tester where LEDs could be exposed to hundreds of volts in reverse, I didn't wait to see smoke, but used steering diodes, or anti-parallel LEDs back to back to prevent exposing them to high reverse voltage. A nice benefit from using two LEDs back to back with AC is you get twice the light for a nominal peak current, an issue with my outlet tester since I wanted to keep ground current < 5mA to prevent tripping GFCI.
JR