the one chopped end is usually due to wear. What often happens is that the carpet wears at the ends and sides first.
Every so often you'll see the sides of rugs shortened too, but it's more usual at the ends because of neglect to act quickly and make preventative measures to keep it from continuing to unravel, especially if not corrected prior to a cleaning. This can be fixed and or prevented by overcasting.
The reason ends are more susceptible is because if you lose a weft, automatically you're exposing an entire row of knots to be lost. Also more importantly, and perhaps most common is that ebay rug sellers may intentionally remove some rows of knots at the end to give the rug a cleaner look. This may be done because of previous damage due to moth, water stain, whatever.
It's sometimes less obvious, and certainly less expensive to remove rows of knots than to make repairs. Even some of the best rugs that have these shorter ends, which sometimes may be considered a sign of neglect on the owner's behalf, however, it's quite apparent that these cheaper goods often feature the shortened ends more often because repairs are less warranted due to low replacement costs.
I can't describe it all that well, but I hope this helps
