Yes, Leo Tolstoy's family is still existing. The Tolstoys is one of the largest family from Russian nobility. There is a record of about 400 direct descendants of Leo Tolstoy living in different parts of the world according to Tolstoys.com. Leo Tolstoy had 13 children, four died in childhood and the rest left Russia because of the aftermath of Russia's revolution.
Some of his famous descendants are: Tatyana Tolstaya, Pyotr Tolstoy, Fyokla Tolstaya and Vladimir Tolstoy. Some of his descendants are in Russia, where they continue to preserve his legacy.