The word "base" refers to loyalty to the family, to the family bond that Ismenia has.
Explanation:
Antigone speaks the words shown above to her sister Ismenia. In these words, Antigone questions Ismenia's loyalty and commitment to the family, using the word "base" to refer to that family loyalty. That's because their brother was banned from receiving a decent funeral, which prevented his soul from being able to rest in peace. The king ordered that whoever made a feneral for the brother of Ismenia and Antigona would be condemned to death. However Antígona, in loyalty to her brother, is willing to take that risk and wants to know if Ismenia has the same loyalty.
I really like the character of Charles in the short story "Charles" by Shirley Jackson. She's a really famous author. He's sneaky and totally fools his parents so that they end up looking stupid at the parent teacher conference.