With Faulkner's Emily the restrained daughter of a patriarchal society and Gilman's unnamed narrator as the victim of the femme covert laws of a Victorian Society, both characters lead lives of repression. For, they are not allowed to express their emotions or desires, or needs.
For example, in "A Rose for Emily" when Emily has had suitors, her father has turned them away; likewise, in "The Yellow Wallpaper" when the narrator has a "real earnest reasonable talk" with John, her husband, asking him if she can visit some relatives, he does not allow her to go and refuses to repaper the room, saying that
...nothing was worse for a nervous patient than to give way to such fancies.
Instead, John patronizes his wife, calling her "a blessed little goose." So oppressed is this woman by her husband who will not permit her to walk in the garden or move to another room that she "tries" to exert will power and suppress the tendency to have "excited fancies" as her husband calls them. This suppression, however, leads to distortions of thought. With nothing to relieve her depression Gilman's narrator focuses--psychologically "clings"--to that which has robbed her of the healing aesthetic pleasure she has craved. She obsesses over the pattern of this paper until she imagines a woman struggling behind it to be free.
Similarly, the fancies of Emily in Faulkner's story become so thwarted that Emily partially assumes the appearance of her dead father: "bloated" with a "pallid hue," wearing her father's watch suppressed inside her belt.
...with nothing left, she would have to cling to that which had robbed her....
Having long ago banished the alderman who have come to collect taxes, Emily clings to the past and holds her Northern beau in her barren home where her desires have been repressed. And, in this old, dusty environment of patriarchal oppression, Homer Barron is held captive in death, just as Emily has been captive in life. Deranged by her isolation, Emily lies with Homer’s dead body at night.
Similarly, Gilman’s protagonist finds a deranged meaning in sharing with another—the imagined woman behind the wallpaper. She circles the room, following the pattern of the wallpaper, essentially becoming the woman inside the wall and trapping herself in an endless maze of mental confusion.
Certainly, the oppressive lives of both female protagonists of Faulkner and Gilman lead to repression and, ultimately, tragic ends as both stories examine the position of women in the nineteenth century, a position marked by a damaging patriarchal system and the femme covert laws.