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If you added a song to one of your playlists and then downloaded the playlist while the same song isn't also featured in your downloaded Liked Songs, then the song won't display as downloaded if you look it up through the general Search feature once you removed it from the playlist.
On the contrary, if you remove the song from your downloaded playlist while it's still part of your downloaded Liked Songs playlist, the song will still display if you, for instance, play your Liked Songs while in Offline mode.
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