The men discover a dead body in the upstairs bedroom.
Soon after Emily is buried, several of the men force the upstairs open. There they find what is evidently the rotten corpse of Homer Barron.
There is a corpse in the bed that appears to have been there for quite some time. Miss Emily apparently killed Homer Barron and kept his body in a bed upstairs. The rat poison she buys early in the story is explained (by implication) in the discovery of the dead body in the upstairs bed.
Though the identity of the corpse is not entirely clear, the implication is clear that Emily has killed someone (probably Homer) with rat poison and kept the body upstairs as part of a fantasy romance.
A grey hair, like Emily's hair, is found on the pillow next to the corpse. This implies that Emily has spent time lying or sleeping next to the corpse. As some critics have pointed out about Emily, "She may even be mad..."
The discovery of a dead body and evidence that she was spending time lying next to it certainly suggest a strange fantasy life for her character.