In part IV of A Rose for Emily by William Faulkner we learn that the portents of Homer marrying Emily were very scarce. Nevertheless, he would drive her around town in a way that was beginning to cause unrest among the people, feeling first sorry for Emily, but then declaring that this open courtship that is going nowhere was setting a bad example for young people.
As a result, the minister's wife calls in Emily's cousins. The townsfolk believe that the purpose of the cousins being there is to assure a marriage. Indeed, after they leave, Homer is seen entering Emily's house for what would be the last time ever; this seals the idea that he had left previously to prepare for the wedding and wait until the cousins leave. In fact, the townsfolk narrator even sides with Emily saying "enough with the cousins", so that Emily can have her day at the altar.
Two days later we learned that she had bought a complete outfit of men’s clothing, including a nightshirt, and we said, “They are married.” We were really glad. We were glad because the two female cousins were even more Grierson than Miss Emily had ever been.
This comment about "being Grierson" evokes the original father of the clan, and Emily's father. The man, who kept Emily overprotected for so many years, made a recluse of his daughter for his idea that nobody was ever good enough for her. As he imposed his will upon his daughter, he took away her own. This is why the townsfolk sided with Emily: they saw her as a victim of her father's strong will.
Yet, when the townsfolk believed that the cousins came to force Homer to marry Emily, the town realized that the very strength of character that Mr. Grierson had sucked away from his daughter was still imminent in the other members of the family. As a result, the town erroneously concluded that the cousins used the "Grierson way" to make Homer do what Emily could not make him do: to do the right and honorable thing and marry Emily. In that sense, they were "more Grierson than Miss Emily had ever been".
In order to see why the townspeople are glad that the Grierson cousins fail, we need to understand why the town sent for them. In Book III, the town appears to be happy that Emily and Barron are seen together,
But there were others, older people, who said that even grief should not cause a real lady to forget noblesse oblige--without calling it noblesse oblige. They just said, 'Poor Emily. Her kinsfolk should come to her.'
The phrase noblesse oblige is French for the obligations of nobility. In this context, the townspeople are offended by Emily allowing herself--an aristocrat--to be courted by the worst possible suitor, a Yankee and a day-laborer, a man far below her station. Even though she is now poor, she still is the last representative of the town's ruling class, and marrying below her class is seen as a violation of her social responsibility to marry an "equal," which Homer Barron is emphatically not.
Although the town's attitude toward Emily's courtship is ambiguous--some people are happy for her, some are opposed to the marriage--the town finally concludes that the relationship is improper, and the minister's wife calls in the Grierson cousins from Alabama to convince Emily to break off this relationship:
So she had blood-kin under her roof again, and we sat back to watch developments. At first nothing happened. Then we were sure they were going to be married . . . . We were glad. We were glad because the two female cousins were even more Grierson than Miss Emily had ever been.
Because the two cousins apparently fail in their task of convincing Emily not to marry Barron, the town is pleased not because of the apparent marriage but because the town really dislikes the Grierson cousins' aristocratic manner. Earlier in the story, for example, the town-narrator comments that the "Griersons held themselves a little too high for what they really were." Because the town itself is not truly concerned with Emily's happiness, it would rather see the aristocratic Grierson cousins fail that to see Emily married.
One of the important themes in the story is the conflict between the New South, represented by the town, and the Old South, represented by Emily and, later, the Grierson cousins. The town still respects the Griersons, but it does not like the Griersons as representatives of the pre-Civil War aristocracy. The town, therefore, even though it does not support the idea of Emily marrying below her station, hates the aristocratic Griersons even more, and the town is happy to see the cousins, who apparently exhibit even more aristocratic qualities than Emily, fail completely.
This episode illustrates the class struggle that is playing itself out between the town and Emily and, like other episodes in this conflict, Emily gets her way, but in a horrific "victory."