"My Dead Friend" is a song Trent Reznor hinted at in a pre-With Teeth interview. It has not been released, along with several other With Teeth-era songs: "The Warning," "Message To No One," and "The Life You Didn't Lead," all hinted in PDF lyric sheets and posters.
Although only speculation at this stage, the 2017 song This Isn't The Place lyrically matches the song title quite strongly.