The very premise of this story lies on a symbolic principle. In fact, the story is almost held together by symbolism, so you can probably analyze any object (or character) of importance in the story and assume that a symbolic meaning exists there.
To get you started consider the symbolism involved in the act of "sin-eating" itself:
- "The sin-eater": a person who performs a spiritual ritual of "eating" the sins of a dead person so that his soul can go to heaven.
- the bread the sin-eater eats: symbolic of sin
Other elements in the story that could be considered symbolic are:
- Joseph's name: possibly symbolically linked to the Joseph of the Bible - Jesus' earthly father. In this way, the religious allusion here is a symbolic effort to show the vast differences between this character and the Biblical figure.
- Joseph's profession of psychiatry: though Joseph is opposed to the idea of "sin-eating," his profession is very similar in that he listens to and takes on his patients problems (sins) while they are still alive.
- flower symbolism: the calla-lillies that Joseph grows are symbolic of his desire for positive change; the stolen-sunflower could be symbolic of the "stealing" of Joseph's ability to maintain fidelity
There are several other symbols throughout the story that you could add to this list. Many of the objects have symbolic meaning outside of the story's context that could be applied to further understand the meaning of the story.