William Faulkner liked to write about odd, strong-willed "survivors." In what ways is Miss Emily a "survivor"?

To add to the excellent responses above with specific examples, you could examine how she survived her father and his scrutiny over her suitors.  She survived the disgrace of her betrothed abandoning her (and through her strong-will got revenge).  Another example is how she absolutely refused to pay her property taxes.  The former mayor once, because of an obligation to her father, made her exempt from property taxes.  However, once that mayor is gone, the preceding ones try to get her to pay the taxes, once even venturing to her house and sitting down with her, but through her strong-will and utter refusal, they eventually cave and allow the old tradition to exist.  That incident reveals a lot about Emily's character.