If she genuinely loved me, and was genuinely well-to-do, she could provide me with the resources needed in order to rise above being homeless and poor. I could move into her house, get cleaned up, have an address I could use for job applications, and I probably wouldn't be above taking a job at her profitable business.
For what reason would I remain homeless/poor/socially unacceptable if there were a successful woman who loved me anyway?
I could certainly understand her not wanting to share my past with her family and friends. I may well not want her to do that, either. And I might prefer to be introduced to her friends and family once I was able to get to a point where it wouldn't appear as if I were just sponging off of her.
And it also goes to why I'm homeless in the first place. A lot of homeless folks become homeless because they lose a job, or their car konks out on them and they lose their job, or what have you. It's a temporary situation for them, and they will struggle as best they can to improve their situation. In other cases, people become homeless because they have some sort of psychiatric disorder or substance abuse problem that interferes with their ability to take care of themselves.
The various potential factors make it a difficult question to answer.