There is no evidence in the story that Miss Emily supported herself financially in any way other than through her china-painting lessons. We can assume that she had always lived off the money left to her by her father, and we know that it must have been a limited amount. How she managed to pay her manservant, Tobe, and supply herself with food is unknown. She may have simply refused to pay her bills as she refused to pay the taxes on her property. She had no friends, so she probably did not borrow money from them or from a bank;
Not that she would have accepted charity.
and there is no mention of her selling off items within her home.
When her father died, it got about that the house was all that was left to her... Being left alone and a pauper, she had become humanized. Now she too would know the old thrill and the old despair of a penny more or less.
Since her needs were few and she never left the house, the small amount of money left to her by her father may have sufficed until her death.