Yes, they are repairable. A pipe repair person can snug a nickel or silver band around the shank there and make the stem fit again. Of course it's up to you if the repair is worth it to you or if you don't mind the metal band. Norwood's Pipe Repair costs $18 for a nickel band and 21.75 for a silver one.

Edit: And you can do this yourself if you're inclined. Vermont Freehand or Lowe Pipe Repair Supply sells the bands.