Miss Brill is an aging, lonely teacher from England who has moved to Paris to teach English. She also reads to the elderly (we presume this is a voluntary activity), and exists in what is known as "genteel comfort" living in a small apartment described as the size of "a box".
By "genteel comfort", what is generally meant, is that she may appear in the outside to be in a somewhat fit financial status, not because of what she has, but because of how she acts. She does show sensibilities often attributed to people with money, such as her love for the theater, her knowledge of music and, of course her knowledge of a foreign language that she can even teach.
As an expat (British expatriate), however, we doubt that she had found any comforts or luxuries that would render her able to return home and live in comfort. Hence, the fact that she can only afford to live in a small room inside a boarding house. Her "treats" are also quite economical. Going to the baker's once a week on a Sunday to get a piece of almond bread is far from glamorous. Moreover, why is her fur still in such a detestably worn out condition?
Our conclusion can only be that Miss Brill has, perhaps, had a good education that has allowed her to extend her knowledge onto others. Like most teachers, however, she cannot expect to become rich by being an educator. Hence, she works, lives out of a small apartment, enjoys small comforts, and bypasses any costly amusement, such as the opera or the theater, in favor of people-watching at the Jardins Publiques.
Undoubtedly she is a woman with limited financial means making the best of what she can.