…than the nearly used up bar? Isn’t it all the same soap? Has the remaining sliver just been leached of all its soapy goodness?
Chances are, it isn’t soap, but rather a synthetic detergent. But that wasn’t your question.
One aspect is that a mostly used bar has a significantly smaller surface area than a new bar. So trying to create a lather would require more linear displacement to remove the same amount of material. In other words, you have to rub it more to get the same amount.
Some of the components in a bar of “soap” are more volatile than others; read the very long ingredient list on a new box some time. It may be possible that some parts of it leech out of the bar before the end; the sliver left at the end does seem dryer than a new bar.
If you have hard water, there may be a slight scum of calcium or other ++ ions adhering to the surface of the soap. Break it open (or scratch the surface off with a knife) and see if the untried surface is as soapy as a fresh bar.
The soap has a higher moisture content when you just take it out of its wrapper. As it sits and dries during the time you’re not using it, it makes it a little harder each day to rub enough off the bar to make a frothy lather.