If you added a song to the library, and you delete the original
song file from the HDD itself instead of the library, the song will
be listed as a broken link in library, meaning it cannot be played.
This is because the songs listed in library only acts as a link to
the original song file.
The reason why it can still be playing even though you deleted it
while its playing is because whenever you play a song in WMP, it
retains the song file until the player is closed or it changed to
the next song. This is why when you delete a song file while it is
playing, when you come back to the folder a while later, you'll see
the song file there again. It'll disappear the moment WMP is
closed.