I'm writing a book and I need a word to call a character who is punished for becoming part of a group of people who are socially rejected and unwanted. They are left to fend for themselves on the street.
It looks like you already have one. "Pariah".
If you're looking for a similar word with less of the specific connotations of 'Pariah', then the word 'outcast' would probably suit your needs.
One who is forbidden from a group out of shame could also be said to be "banished" from the group.
You might want to use ostracized, it fits perfectly:
ostracize, ostracise [ˈɒstrəˌsaɪz] vb (tr)
1. to exclude or banish (a person) from a particular group, society, etc.
2. (Historical Terms) (in ancient Greece) to punish by temporary exile
[from Greek ostrakizein to select someone for banishment by voting on potsherds; see ostracon]
One particular term for individuals who are outcasts is untouchable, used as a noun.
a member of the lowest-caste Hindu group or a person outside the caste system, contact with whom is traditionally held to defile members of higher castes.
While often applied to the Dalit community in South Asia, this term is used for various groups in other countries as well. See discussion here.
outcast 1: one that is cast out or refused acceptance (as by society) : pariah
Leper would work. Note the 2nd definition from M-W:
Definition of LEPER
1 : a person affected with leprosy
2 : a person shunned for moral or social reasons
You could also describe the character as a social leper.
"Untouchable" was one of the suggestions, and it fits nicely, especially with ethnic connotations.
On the other hand, "untouchable" can also have a nearly opposite meaning, someone or something that cannot be equaled, especially in a competitive setting. It was also the nickname of group of Federal agents in the US because they were not susceptible to graft.
It's all in the context.
An interloper is a person who becomes involved in a place or situation where they are not wanted or are considered not to belong.