I see the relationship between Emily and Toby. In the early part of the story it discusses that Colonel Sarttoris believes that 'no Negro woman should walk the streets without an apron" is this quote mentioned in the story because Emily is of mixed race?
The major mention of race is that of the servant Toby. The fact that he had to have known al along that Miss Emily killed her man and was sleeping with the body yet he did nothing to try and either have the body removed or alert the authorities to the situation speaks volumes of race relations at the time, to me. He slips out the back door after her death running away, it seems, so that he will not be implicated in what he knows was a crime, yet he was a silently willing participant in it. Why? Because he was a black man in a white person's world. His job, his place in life, was to do as he was told by Miss Emily and to do it loyally and without asking questions.
In all of my readings, I am not able to recall any implication that Miss Emily is of mixed race. To the contrary, she probably would not have wielded such power over the community if this had been the case. The comment is more likely meant to inspire observations about Colonel Sartoris’s character., and it could have some connection the the Faulkener novel, Sartoris.
The irony of slaves' relationships was most pronounced with those who worked and lived in the houses of wealthy Southerners. For, often they were treated much like members of the family. As children they played with the owners' children, the Mammy was much like a mother in advising the child as well as physically caring for him/her. The house servants were often privy to family-related discussions among the owner's wife and children; children often confided in their maids, or mammys. This relationship is exemplified by Harper Lee in her novel "To Kill a Mockingbird" although Calpurnia is a free woman.
Old Toby may easily have grown up with Emily; he probably talked with her and genuinely cared for her. When Emily dies, he knows that all ties to the house and family of Grierson is cut, so he leaves.
There is no reason to believe that Emily was of mixed race. There is every reason to believe that she was white, the daughter of a once prominent family in Jefferson that dated back well before the Civil War. The reference to requiring that "Negro women" wear aprons in public concerns an edict that Colonel Sartoris issued in Jefferson shortly after the Civil War ended, and it is included in the story only to develop the history of Jefferson and establish its cultural roots. Emily's "man" Toby (a common slave name) had no doubt been a servant in the Grierson house for many years, but he was free to leave, and he did exactly that as soon as she was buried. When the people of Jefferson came through the front door of Emily's house, he walked directly out the back door.