In the Prepare to Die Edition, the player has an opportunity to save a young Sif from the Abyss. After doing so and summoning Sif for a boss fight deep in the Abyss, if the player has not yet defeated Sif in the present, the opening cutscene will change.

Sif appears to recognize the player, and is reluctant to do battle with them, but finds it necessary, likely due to Sif swearing to protect the grave or the Covenant of Artorias. This cutscene makes the hobbling animation when Sif is at low health even more heart-wrenching for some players.
Contributed by TomGuycott