In the story A Rose for Emily, several personality traits may have allowed her to continue to live a life as if nothing had happened out of the ordinary in terms of the death of her longtime companion Homer Barron.
First, Emily was strong-willed and stubborn. This, we can see in the way that she refused to pay taxes for her family's old connection to the old Colonel Sartoris. She is also strong-willed and stubborn in letting time pass and change to take place. Her home, her demeanor, her behavior and her mentality was the same as she had since she was a young woman with money in a powerful family. Now, times changed and she remains in the same psychological niche.
Second, she is in denial- When her father died she had a hard time letting go of his body and after his burial she had an even harder time to accept that he was gone. She continued with the sheepish and shy attitude of a woman whose father is controlling and looms over her existence.
What this has to do with Homer's death is that both her strong-will, stubbornness, stuck-up ways, and the outstanding ability to deny reality mixed up perfectly to help her imagine that things were alright, even when the corpse of Homer Barron was laying next to her in bed every night, even though she killed him with arsenic, and even though she was well-aware of it. It was her personality which made her the unique and eccentric person that she was.