Homer Baron mysteriously disappears and everyone in the town assumes he has gone back up north where he came from...however, we know that from the poison Emily buys for "rats" and the lye the men put around her home to get rid of the awful smell, and from the skeleton in her bed with the "iron-gray" long hair on the pillow next to it, that she killed him and kept him in her boudoir until death made them part ways.
Of course, it's all circumstantial evidence (except for the skeleton, of course) since he may have had a massive heart attack and she just chose not to tell anyone since they would have taken him away from her like they did her dear old dad when he died. She chose to keep her mouth shut and take care of him in her own way.
The readers are forced to speculate about most things in this story. The narrator tells us the story in a zigzaw style forcing us to put the puzzle pieces together and draw our own conclusion. Now, if Miss Emily wanted the arsenic to kill rats, what's so hard in admitting that to the druggist? Miss Emily probable fed that arsenic little by little to Mr. Homer until he succumbed to its effect. Miss Emily was not about to let anyone rob her of her of her new found relationship, so she had to be proactive couldn't leave that to chance. She had become a disturbed woman, capable of doing anything.