Here is a description of just how vast the scattering of Israel has been. These lands stretch from Africa to Asia and Europe. But that is not all, because they also include "the isles of the sea." And, as Nephi has informed us, the Americas are part of the "isles of the sea." Significantly, all mankind's bloodlines, from Ham, Shem and Japheth, are included in these scattered lands. All these lands and bloodlines have been mixed with the scattered bloodlines of the lost Israelites. We can see from this just how broad the promise to Abraham really was. The Lord has now accomplished His promise that "all nations" would be blessed through his bloodline. With the Restoration of the Gospel, the Lord is now completing the cycle and bringing these descendants back to the knowledge of their relationship to Abraham.
The "remnant of his people which shall be left" include people who are located literally all over the globe. They are in every nation of the earth. But as a "remnant," they are not aware of their status. Therefore, it is necessary for the "root of Jesse" to "set his hand again the second time to recover" them. He will have to set His "hand" because He will have to intervene to accomplish this. It will not happen without His direct involvement. He will have to do it the "second time," because Israel, in their scattered state, must be taught their identity which they have long ago forgotten. It is Nephi's testimony in Isaiah's words that the latter-day restoration of the Gospel, and the founding of the Church of Jesus Christ of Latter-day Saints, is a work which God's own hand will accomplish. Through it, Israel as a people will be reclaimed.