In the story " A Rose for Emily" by William Faulkner, the main character of Emily Grierson, also known as Miss Emily, is meant to represent a far-gone society refusing to accept the changes that come with the passing of time. Miss Emily's character also embodies co-dependence, terror of change, the inability to move on, and the refusal to let go of the past.
This means that the character of Miss Emily gives Faulkner an ample array of possibilities for using literary techniques, namely symbolism, to add mystery and (as your question states) depth and sophistication to the story. After all, the story is a representative of Southern Gothic literature, which means that symbolism is a required, if not expected, literary element.
One example of symbolism is found when Miss Emily's house is described as "an eyesore among eyesores". This particular home is described as one who once was regal, sumptuous, and respectable. Yet, as time changed around the Griersons, the house (and those in it), became archaic.
The description shows that the past is now gone for good, and still Emily intends to stick to what once was, without being successful.
It was a big, squarish frame house that had once been white, decorated with cupolas and spires and scrolled balconies in the heavily light some style of the seventies, set on what had once been our most select street. But garages and cotton gins had encroached and obliterated even the august names of that neighborhood; only Miss Emily's house was left, lifting its stubborn and coquettish decay above the cotton wagons and the gasoline pumps—an eyesore among eyesores. And now Miss Emily had gone to join the representatives of those august names where they lay in the cedar-bemused cemetery among the ranked and anonymous graves of Union and Confederate soldiers who fell at the battle of Jefferson.
Another interesting and symbolic episode occurs when the town of Jefferson, in moving on with the times, began getting mail in a new way:
When the town got free postal delivery, Miss Emily alone refused to let them fasten the metal numbers above her door and attach a mailbox to it. She would not listen to them.
Both of these examples are symbols of how Emily represents an inability to let go of the past, and the fear that inhabits every person about moving on and getting on with the times.
Finally, there are several times in the story when the "closed doors" in Emily's house is continuously mentioned. One remarkable part is when it says that, when people stopped going to her painting lessons, and she closed the door, forever.
The front door closed upon the last one and remained closed for good.
This is a symbol of the most salient theme in the story, which is isolation.
In all, Faulkner uses common objects and actions in a way to represent other things and instill in the reader curiosity and mystery as well as sophistication and depth.