Are you sure that yuo have images with the Y, yy and yyy keywords assigned? When you click the arrow next to yy, or next to yyy, do any images show then? If not, then it will be appropriate for a keyword search on Y (which is what clicking the arrow means) to produce zero results.
When it comes to nested (hierarchical) keywords, it is possible for the same keyword name to appear more than once in the overall list. Could that be a source of confusion here? For example: there may be a top-level keyword "France", with some keywords nested inside including one named "Paris": and there may be another top level keyword "Texas" with its own nested keywords inside, including one named "Paris". There may also be a top-level keyword named "Paris". These three are logically and practically separate, even though their immediate names are identical.
Analogy: many different families can all include a son named Patrick, without conflict or confusion, because we know these are different Patricks, which can be told apart by giving both first name and family name. And in the Lightroom example, one keyword is "Paris < France" - one is "Paris < Texas" - and one is "Paris". Different keywords.
In my opinion it is not helpful to use the concept of a "folder" for these logical and virtual functions. The hierarchy / parentage of a keyword, is one of the attributes of the keyword itself. And remember: each image may have many keywords at the same time, offering both independent and combined means of organisation.