From the Rebbe's words at a farbrengen, Tammuz 12, 5711 (July 16, 1951), several months after the passing of his predessesor, Rabbi Yosef Yitzchak of Lubavitch.

There are those who have questions regarding the Rebbe's passing...

The Talmud says regarding the judge Samson: "One verse states that he judged the people of Israel for forty years, while another verse states that he judged the people of Israel for twenty years. This is to teach us that they feared him for twenty years after his death just as they had feared him for twenty years in his lifetime." In other words, since his effect of his leadership continued for twenty years after his passing, his leadership extended throughout that period, and the Torah considers it that he judged Israel for forty years.

If the above applies to a judge, how much more so does it apply to a Rebbe, whose soul embodies the yechidah (the quintessential core) of every Jewish soul, so that the whole concept of a "passing" is not that applicable.

There are areas in which the Rebbe's passing has significance. But in all that pertains to his leadership, nothing has changed. Just as all our activities have met with supra-natural success two, three, four and more years ago because they were led by the Rebbe, so will it be in the future: the Rebbe continues to lead us.

There has been no end to the Rebbe's life, G‑d forbid. There is no "legacy"a concept which implies an inheritance to be divided up, each one picking and choosing what he desires to take for himself from it. Rather (as our sages say regarding Jacob), "he is alive," and continues to lead us and direct everything.