Some background on Pierre: He never got around to deciding on a career in the short time he was in St. Petersburg. He was then kicked out of the then-capital by reason of the scandal involving tying a police officer to a small bear and throwing them both into a river. 

In Moscow, Pierre was staying in his usual quarters at the estate of his ill father - Count Kirill Bezukhov. However, Pierre was not allowed access to his dad. Pierre was isolated by the Count’s relatives and servants. Early in his stay, he went to see his cousins, referred to as the “princesses.” They are three young women who are the Count’s nieces and were also staying at the house, ostensibly caring for the Old Man. Pierre kindly asked the princesses how they were doing, if they remembered him and when he could see his father. They gave Pierre the blow-off. This group is hoping for a large bequeath upon the Count’s death. 

Prince Vasili Kuragin also met with Pierre, ever so briefly, only to lecture him that he will come to a bad end if he continues to behave like he did in St. Petersburg. Vasili is hoping to take the Lion’s share of the estate, given he is a relative to the Count through his wife and the Count doesn't have any legitimate children. 

Pierre did not have any further visitors until the day Anna & Boris visited. Boris appears at the door while Pierre is in a world of his own, pretending to be Napoleon - Yes, Pierre admires him that much! Pierre is acting out having crossed the English Channel and successfully defeated the English. He is about to pronounce sentence on William Pitt…when he notices Boris in the doorway. Historically, Pitt was a well-known Prime Minister, famous for his length of service and administrative acumen.  

Boris announces his presence but Pierre does not recognize him. He suspects that he was once familiar with the lad. He initially mistakes Boris for one of the Rostovs. When Boris reveals who he is, Pierre is genuinely happy to remake his acquaintance. Such is Pierre's nature. Pierre tries to get the conversation going by focusing on world politics but Boris concedes he doesn’t know much about current events and keeps occupied with the affairs in Moscow, which includes dinner parties and local gossip. Boris reveals all Moscow is guessing who will get the Count's estate as beneficiary and many think Pierre is a candidate. Pierre is somewhat fearful Boris would say something that will embarrass himself but is ultimately impressed with his candidness. Boris notes that he and his mother will not be pursuing such claims. He feels they do not deserve any financial windfall as they are not true relatives. Pierre hopes he and Boris become fast friends. 

There is an interesting contrast between Pierre and Boris:

Pierre went off the Europe and became a worldly man - in the early 19th century sense. He comes home and is indecisive about what he will do. He has ideals and vague plans. He is a student of the French Revolution and Enlightenment. He is enthralled with Napoleon and wants to shape the New World but doesn’t know in what way. 

Then there is Boris, who has remained home and doesn’t have the same level of prospects or confusion. He has a mother without funds, but she was able to put her son on a steady career path in the Imperial Guard (a better position than Pierre or Nikolai currently have). Boris is grateful for the opportunity, accepts his lot, and out of a sense of personal honor, does not want to squander his chance.

A footman calls for Boris as his mother is ready to leave. She tells Prince Vasili she will be back to attend to the Count and prepare his soul for it's ultimate journey.  While Boris and his mother exit, Anna reveals the Count appears close to death.