Elizabeth Willard's legacy to her son George is twofold - the first is the desire to leave Winesburg in search of something better, and the second is the eight-hundred dollars she has been saving for him, that will enable him to start a new life somewhere else.
Elizabeth is a bitter woman, frustrated because she has allowed that "secret something that is striving to grow" within herself to be stifled by misguided choices and the resulting life of inertia in a stultifying town and a marriage ultimately loveless and unfulfilled. In her son, she recognizes the same longing for something more, that defines her own life. This awareness of the void, along with the desire to find a way to fill it, is part of her legacy to her son.
Elizabeth's father, too, had been aware of the fruitlessness of his existence in Winesburg, and had begged his daughter not to stay and marry Tom Willard. The old man had saved eight hundred dollars, and, on his deathbed, he had urged his daughter to "take it and go away." Elizabeth had not followed his directive, but later had realized that her father had been right. She had hidden away the eight hundred dollars, so that her son might use it to do what, sadly, she had not.
It is ironic that, in the end, Elizabeth is ineffectual in following through in giving the gifts of her twin legacies to George. In "Mother," George confides to her that he has indeed decided to leave Winesburg and seek his fortunes elsewhere, but Elizabeth does not respond encouragingly, even though she means to - "she want[s] to cry out with joy...but the expression of joy [has] become impossible to her." Instead, she indifferently brushes off her son's dreams; Elizabeth herself is so broken that she is unable to affirm that for which she most yearns - the possibility of salvation for her son. In the same way, the eight hundred dollars she has painstakingly hidden from her husband and saved for George all those years is also lost to him. Elizabeth has never told George about its existence, and is rendered speechless by a stroke in her dying days. As recounted in "Death," George never learns about the legacy that his mother, throughout her lifetime, has so carefully guarded for him.