I’m not sure why you think she needed to come from a well-off family to be connected to this address. In fact it seems to have been quite the opposite.
Sarah Featherstone had been in the Southwark Workhouse in November 1899, and in Jan 1898 in the Holborn Workhouse. It makes sense that she might be in this establishment for “women in need” in 1901. She was possibly there only a short while.