The Lumpenproletariat (directly translated: rag-proletariat) is a term used by Marxists to describe the section of the proletariat that can't find legal work on a regular basis. These may be prostitutes, beggars, or homeless people.
... and Vronsky are at the station to welcome Anna and Vronsky's mother respectively. This is the occasion the first meeting of Anna and Vronsky. As they, Anna and Countess ...