It has been said of this story that "Miss Emily has a shadow, and by this shadow we tell the time of her life." What is her shadow?

Your question is from a study guide from Dr. Tina Hanlon, Associate Professor of English at Ferrum College (see below).

She does not cite a source, so we do not know who originated this quote or who the "we" is.  "It has been said..." is rather vague.

The word "shadow" is mentioned 3 times in Faulkner's story, "A Rose for Emily."

Before the murder of Homer:

They called a special meeting of the Board of Aldermen.  A deputation waited upon her, knocked at the door through which no visitor had passed since she ceased giving china-painting lessons eight or ten years earlier.  They were admitted by the old Negro into a dim hall from which a staircase mounted into still more shadow.  It smelled of dust and disuse-a close, dank smell.

Shortly after the murder:

As they recrossed the lawn, a window that had been dark was lighted and Miss Emily sat in it, the light behind her, and her upright torso motionless as that of an idol.  They crept quietly across the lawn and into the shadow of the locusts that lined the street.  After a week or two the smell went away.

And after Emily died:

And so she died.  Fell in the house filled with dust and shadows, with only a doddering Negro man to wait on her.  We did not even know she was sick; we had long since given up trying to get any information from the Negro.  He talked to no one, probably not even to her, for his voice had grown harsh and rusty, as if from disuse.

Emily's "shadow" is her death, her past, her father's death, Homer's death, the decay of the South, the secret of Emily's upstairs bedroom where she committed murder and necrophilia.  It is a kind of Gothic imagery "catch-all."