What about southern culture made it believable that Ms. Emily would die with her home and secret intact?
One of the themes of this story focuses on the decline of what is known as "The Old South". Faulkner was one of many Southern writers to address this in his fiction. The pre-Civil War South was a society of strict social traditions and strata. Ladies were pampered, they did not go out in the sun, they wore white gloves, men were expected to treat them in a respectful manner, they did not work, they were wives and mothers, and if their husbands had multiple "liaisons" with their black slaves, the women looked the other way. Certain things were just not discussed in polite company. An unspoken code of chivalry was expected and the roles of women were narrowly defined. This is why Colonel Sartoris does not collect taxes from Miss Emily and makes up a fantastic story to explain his actions.
Miss Emily is of the old generation, and when her contemporaries all die off, the new order wants to change things up. While she lived under the old order, however, people would not think of invading her privacy, so they left her alone, assuming she wanted it that way. They would never have wanted to embarass her or expose any of her secrets. Everything was very hush-hush. Miss Emily came from a respected, well-to-do family, and rather than expose her strange ways, the people of the town covered things up. People preferred that others did not know their business, so it is very believable that Miss Emily would have died alone like she did. The Confederate soldiers that attend her funeral are symbolic of the Old South which no longer exists.