A symbol is an object that stands for something other than it is. An object that symbolizes a character will represent the character in some way.
Jan is a Communist Party organizer, so it might be fitting to have him represented by a Communist Party membership card. Important communist party members often carried membership cards, and Jan was an organizer.
Jan gets annoyed when Bigger tells him about a riot where his father was killed.
That’s why we Communists are fighting. We want to stop people from treating others that way. I’m a member of the party. Mary sympathizes. Don’t you think if we got together we could stop things like that? (Book 1, p. 75)
Jan is also Mary Dalton’s boyfriend. Mary Dalton is rich, so she might have given him an expensive gift, such as a pair of cuff links. Cuff links are expensive, and it is the type of gift that a rich girl might give her boyfriend.
Bigger tries to frame Jan for murder. It is actually Bigger who killed Mary Dalton by smothering her with a pillow. It was an accident. He covered her face with a pillow because he did not want her to talk because Mrs. Dalton would figure out she was there. I am not really sure if a pillow is considered a small object though.