One should be careful of hunting for symbols. The enotes Study Guide on "The Shawl" gives an excellent summary of how critics have attempted to proclaim symbols in the story, which the author herself has denied the existence of and has labeled "pop psychology." Of course, an author's intentions are not definitely the final word on a story, but in this case her statements seem logical.
In short, the shawl--the dominant object in the story--does not symbolize something concrete. It does symbolize several abstract ideas. To Rosa, the shawl is what keeps Magda safe (it hides her). To Magda, it is her security blanket and that which takes the place of food (she sucks on it, instead). To Stella, it is the safety and security that comes with being a baby in a mother's arms, and, later, it is that which will keep her warm.
The shawl is an image, a symbol, and probably an objective correlative--an object that evokes an emotional response in the reader following the chain of events the object is involved in. In this case, the reader experiences the shawl protecting Magda, being an object of envy for Stella, being stolen from Magda by Stella, resulting in Magda's death, and, finally, being used to cover Rosa's scream.
And, of course, all is for nothing. In the face of prejudice and hatred and violence such as portrayed in this story, the shawl cannot save the baby.