Elizabeth March, called "Beth," and the circumstances of her death in Louisa May Alcott's book Little Women, is based on the real life sister of the author. Louisa May Alcott's most beloved sister, Lizzie Alcott, was the "real" Beth. Lizzie Alcott died of scarlet fever when she was twenty-three.
In the fictional story, the circumstances are mostly the same. Beth March, who has dedicated her life to quiet and unassuming charity, is visiting the Hummels. The Hummels are their neighbors, a poor German family with a widowed mother and six children. They live in dire poverty, and the Marches often provide them with gifts of food, firewood, blankets, and other necessities. When the children contract scarlet fever, Beth goes to help nurse them, fully knowing that she is at risk. Her self sacrifice is enormous.
Beth contracts scarlet fever from this, and becomes terribly ill. The family, especially Jo, nurse her back to health. However, although she gets over the scarlet fever, her health is NEVER the same again. She is permanently weakened by this illness. Over time, she becomes weaker and weaker and sicker and sicker. The family grieves, eventually realizing that Beth will not live for much longer.
Her death is the main tragedy of the novel. Although Beth seems to have the least agency of all the sisters, being the most shy and unambitious one, she is the one to have the most impact on the others. She is angelically selfless, and absolutely unconditionally compassionate at all times in her life. Even as she lays in her bed dying, she knits and sews clothes for the neighborhood children.
In conclusion, Beth March (mirrored by the real-life Lizzie Alcott), does not die directly from scarlet fever, but dies some time later of complications from scarlet fever.