The final "Late Show" is scheduled to air May 20, after which Letterman has said he is retiring from late-night television.
Crystal, a Tony winner for his Broadway solo show 700 Sundays, has been a frequent guest on the show over three decades. He showed a montage of clips from his appearances on the show, then did a live performance of the Fiddler song with irreverent new lyrics by Tony-winner Marc Shaiman to replace the Sheldon Harnick originals, accompanied by singers in shtetl costumes.
Sample lyric: "You survived shingles and a bypass/Proving you actually had a heart."
The Bock & Shaiman song begins at the 2:00 mark.