The Pig Ring is an item you get mid-late game by searching through the pot on the stove in the kitchen with the Gold Chopsticks, after turning off the stove and lifting off the lid of the pot. These are found in an adjacent room that was not present the last time the Kitchen played a vital role to the story (lending the cook a hand to receive the Silver Key). This room is filled with skeletons, all of which are missing hands.
After fishing up the Pig Ring from the pot the player must go to the room with the statue of a sobbing woman. The player must then give this woman her ring, and the lady will state,
"... ...This is my...
In return for her ring, this statue will unlock the door to the next area.
You can enter the locked area without giving her the ring but that will kill you.
The ring's in-game description states, "It's blackened and smells foul."