Shalom ,Would you kindly explain under what conditions [pikuach nefesh maybe] if any, does the Halacha obligates us to give our Land of Eretz Yisroel? I vaguely remember once being told that if we know that "if even one person will be killed" we are obligated to liquidate the Land .

Since there is an obligation even to go to war to liberate the Land of Israel (Ramban Mitzvot Asei 4) and to defend our sovereignty in our homeland (Rambam Hilchot M’lachim 5 1), “pikuach nefesh” of the individual does not release us from this obligation (see Minchat Chinuch 425 3). As you must realize, if what you recall being told were true, it would be impossible for the nation of Israel to have a Land at all. Even at the time of Joshua and King David maintaining our sovereignty required us to go to war and the lives of individuals were lost.