They end up on an island with Kit Snicket's baby who is called Beatrice and Olaf died from a wound caused by a harpoon. Kit died of the fungus/childbirth; Olaf ate the remedy so the fungus had no relation to his death. Both are buried on the island. The Baudelaires and Beatrice take a boat (also named Beatrice) back to the 'real world' as they feel they should not shelter themselves or the baby from the treachery of the world (they believe this to be in line with their deceased parents' wishes for them).
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In the final book of "A Series of Unfortunate Events," the Baudelaire children find closure as they uncover the truth about their parents and embark on a new chapter in their lives. Without giving away spoilers, they ultimately find a sense of resolution and hope after their tumultuous journey of adversity and misfortune.