"Madame de Rênal was faithful to her promise. She did not try in any way to shorten her life, but three days after Julien, she died while hugging her children." (2.45.51)
When all is said and done, Julien gets beheaded and his "wife" Mathilde steals his severed head so she can bury it on her own. She also uses her vast wealth to create a marble tomb for Julien's body. Meanwhile, Julien's other lover Madame de Rênal fulfills her promise not to kill herself after he is gone. But it doesn't seem to matter, because Madame dies on three days after Julien… for reasons unknown.
The fact that she dies while hugging her children leaves us with a lot of questions. Is God (or Stendhal) punishing her for committing adultery with Julien? Does it symbolize how Madame can't possibly go on living without Julien in her life? Or does it just show us that life is totally random and that there's no real purpose or order behind any of it? You'll have to answer these questions for yourself… Stendhal, ever the realist, ain't going to answer it for you.