I have failed to pay for Apple Music, will the playlists be deleted?

If you have a Music/iTunes library on your computer for any non-subscription tracks, you can back it up the same way you back up all other files on the computer. Mac users generally use Time Machine.

If they are subscription tracks that you DL'd for offline listening, they will disappear. If they are tracks in your local library they will still be there but pls make a backup to be sure.