According to Isaiah 11:1, "A shoot shall grow out of the stump of Jesse, a twig shall sprout from his stock." This promise of redemption follows directly on the heels of threatened judgment upon Assyria (Isaiah 5:5-15, 27-34), whose oppression of Judah, so long as it lasted, made talk of redemption a pipe dream, nothing more.
But when the prophetic threat of judgment on Assyria began to become reality, that is, as the Assyrian juggernaut lost control of the West in the 640s, an 8 year old child named Josiah of the lineage of David was placed on the throne. It was a time of crisis. According to Marvin Sweeney, Isaiah 11:1-9 is best read in the first instance as an expression of the hopes and fears of King Josiah’s supporters. There is much to be said for this reconstruction. I discuss Sweeney’s thesis and aspects of the political theology of the book of Isaiah here, here, here, and here.