This is actually a good thing from an environmental perspective. Japan has the type of downpour which can thoroughly drench you (in July for instance), but most of the time you don't need an umbrella. Obviously this means that umbrellas get lost, misplaced, or forgotten. If no one just took any seemingly lost umbrella out of politeness, you would end up with thousands of them going to a landfill.

I had the same thing with my umbrella when I left Japan after a year of studying there. “What should I do with this? It's still a good umbrella.”, “Oh, just leave it at the station, someone will take it.”