With this attachment, the Double-Barreled Shotgun becomes more likely to deliver a one-shot kill on damaged enemies only (at close range). However, the Double-Barreled Shotgun without the attachment already kills undamaged enemies in three pellets and has low enough range to begin with, and therefore this isn't the most effective attachment to use.
Also, although it increases damage at maximum range, the player will need more hits to kill, as the range and accuracy are dangerously decreased from this attachment.
Two Sawed-Off Double Barreled Shotguns are briefly seen in the Call of the Dead introduction scene, being utilized by Michael Rooker. What became of them after the scene is unknown, they are not available in Call of the Dead, nor are they seen or mentioned in-game.