Final answer:
The term synonymous with 'undesirable' referring to an outcast is 'persona non grata'. It is a Latin phrase used in English, meaning 'person not pleasing'.
Step-by-step explanation:
The term synonymous with "undesirable" in the context of being an outcast or exile is persona non grata. This Latin phrase is commonly used in English to describe a person who is not welcome or is shunned in a particular community or society. It directly translates to 'person not pleasing' and is used in diplomatic circles to refer to individuals who are no longer accepted or wanted because of their behavior or actions.