What occupations, according to the housekeeper, do many of these people have?

The young man who has been searching for five months for a girl named Eloise Vashner asks the housekeeper:

“Do you have many theatrical people rooming here?” 

She tells him:

“They comes and goes. A good proportion of my lodgers is connected with the theatres. Yes, sir, this is the theatrical district. Actor people never stays long anywhere. I get my share. Yes, they comes and they goes.”

No doubt most of the "theatrical people" were vaudeville performers. They would rent furnished rooms because they were "booked" on "circuits" and were always on the move, traveling by train from city to city and from town to town, living out of suitcases and eating in diners. In many cases vaudevillians would have a succession of "one-night stands," meaning there were only enough theater-goers in smaller towns to sustain their act for one show and they then had to move on to the next town. Obviously, those who stayed in a rooming-house like the one described in "The Furnished Room" would not be stars. The housekeeper speaks highly of a married couple who went by the stage names of Sprowls and Mooney because they stayed for three full months. Husband and wife vaudeville teams often did "stand-up comedy" routines together.
Eloise Vashner must have come to New York with high hopes of becoming a star as a singer, but her career appears to have gone downhill "...from all-star casts down to music halls so low that he dreaded to find what he most hoped for." New York was a magnet for people with talents of every kind, but the competition was fierce.