This lady, Boris's mom, is a good example of a Tolstoy technique that boosts the realism of the novel. She starts out the novel being a way important character – basically the best at playing the kind of politics that will get her son ahead. Actually, that's kind of an understatement, because she's on another level. After all, she helps Pierre figure out where his dad's real will is and basically gets him the inheritance all because he'll then be in her pocket enough to get Boris a leg up (which he does later on by supporting Boris's bid to join the Freemasons for the networking connections).
After all this awesomeness, though, and after she's described as BFF with Countess Rostov, Anna Mikhailovna just drops out the picture altogether. No explanations, no coming back to fill us in on her doings, no nothing. But isn't that what it's like in real life? People are in your life, and then circumstances change, and they just aren't a part of your world any more.