July/19/2018:
Version 1.2
This component adds two options on Toolbar Menu > Edit.
Remove playing track: it removes the current track on the playlist that it is playing although the playback continues on that song—you still hear the song—.
Remove playing track and advance playback: it removes the current track on the playlist and the playback goes to the next song—you hear the next song—
In both cases, I could not find the option of doing automatically.
Download component page on Foobar Components Repository. (http://www.foobar2000.org/components/view/foo_np_remove)