A little historical background on the events of Isaiah 7:
By the reigns of Pekah the king of Israel, and Rezin the king of Syria, the generation of Assyrian kings that had had repented at the preaching of Jonah had died out. During their lifetimes, as the Assyrian kings no longer went out to war, the Assyrian empire was reduced back down to her old national boundaries. But upon the death of the last of that line of kings, a usurper took his chance, and gained the throne. His name was Tiglathpileser, and he sought to restore Assyria to her former glory, and began again campaigns of conquest.
Israel and Syria had gotten used to their freedom from Assyrian tribute, so when Tiglathpileser again imposed it upon them, they resolved to shake off the Assyrian yoke. They made a league together to revolt against Assyrian authority, and sought to get Ahaz, the king of Judah, to add his strength to their own.
Ahaz refused, and this refusal so angered Pekah king of Israel, and Rezin king of Syria, that they joined together to capture Jerusalem. Their intention was to kill the son of David and put a puppet of their own creation on the throne of Judah, who would do their bidding. Their choice for puppet king was the son of Tabel, whoever that was. The LORD knew who it was and told Isaiah (Isa 7:6). This was the state of affairs when Isaiah delivered his prophecy recorded in Isaiah 7 and 8.
Ahaz and all Jerusalem had (momentarily) repented of their idolatry when Pekah and Rezin had come against Jerusalem to attack it, and the combined armies of Israel and Syria had not yet been able to overcome Jerusalem, but they were strengthening their defenses in Ephraim for a new attack. The house of David was facing its extinction; but the word of the LORD which came to Isaiah, for Ahaz, was to ask the LORD for a sign to prove that he was not to fear either Israel or Syria. When Ahaz would not ask for a sign, the sign that the LORD Himself gave him was:
“Therefore the Lord Himself will give you a sign: Behold, the virgin shall conceive and bear a Son, and shall call His name Immanuel.” Isa 7:14
In other words, the house of David will not cease, but He will be born to David, whom the Law and Prophets testified would come: Messiah, whose name is God with us. For God will be with Him, and through Him, God will again be with Judah, with Israel, and with all mankind. The breach will be repaired!
However, in the mean time, the king of Assyria will indeed come upon Israel and Syria, and their kings deposed, and their people taken captive, so that only a remnant will be left.