Thank you for the opportunity to help you with your question!
I do not believe that poverty will ever be complete eradicated. It is a foolish question to answer without first settling on a definition of what poverty is and is not.
My advocation for an impoverished client would depend on the position from which I am their advocate. This varies: Doctor; lawyer; social worker; case worker. In any of these situations, in fact in all of them, you advocate best by providing them with the service you are able to give so that they may improve their lot in life.
Please let me know if you need any clarification. I'm always happy to answer your questions.