Great, dur(rtfm), so is it save to delete the backup.old, if the db is not in backup mode.
I don't see anything that would cause "backup.old" to be linked to an active backup if there was one in progress...and as far as I can tell a successfully completed backup doesn't leave around any such file either. So it should be safe to delete regardless of what pg_is_in_backup returns. If that returns true then I would be concerned that something (or someone) else is messing with the backup/data directory and that something likely also introduced backup.old