I'm not sure that we know that "the Assyrian" is one person, or one leader.
There is at least one other way prophecies about "the Assyrian" might have been fulfilled. The heartland of Assyria is near Mosul, in northern Iraq. It is possible that the Biblical prophet says "the Assyrian" instead of "the Iraqi" because Iraq isn't in their vocabulary. A ruler of Iraq would be "the Assyrian" because his territory includes the heartland of ancient Assyria.
How does this fit recent history? Iraq was one of the Arab countries which attacked Israel in 1948. While Iraq did not participate in the 1956 war, it was involved in the 1967 war. In 1967, Israel bombed the Iraqi air force and battled the Iraqi Army on the ground. Israel has been at war with both Egypt and Iraq twice, in 1948 and 1967. Iraq was a monarchy until 1958.
Do either of these wars constitute an invasion of Israel from Iraq? Iraqi troops invaded Israel in 1948 but not in 1967. There is one other occasion when Iraq was in conflict with modern Israel. As the 1991 Persian Gulf War loomed, Saddam Hussein fired Scud missiles into Israel. In modern terminology this is not an invasion, it is an attack from a distance. However, in the ancient world there was no way to inflict damage on an enemy from such a distance. To the ancient mind, to say that country A inflicted damage on the homeland of country B would sound like A invaded B. To the ancient mind, Iraq firing long range missiles into Israel would be much the same as an actual invasion of Israeli territory.
When the Assyrian invades our land
and marches through our fortresses,
we will raise against him seven shepherds,
even eight leaders of men.
They will rule the land of Assyria with the sword,
the land of Nimrod with drawn sword.
Micah 5: 5-6 NIV
Could this apply to the First and Second Persian Gulf Wars? It would mean that the Scud missiles fired into Israel in 1991 constitute an invasion. Then Israel's powerful ally, the US, and its allies, invade Iraq, including the core of the ancient Assyrian Empire. Certainly, Iraq was patrolled with "drawn sword" in the aftermath of the Second Persian Gulf War.
Where does this leave us? If Biblical prophecies of "the Assyrian" were not fulfilled before the 20th Century, there is a distinct possibility that they have been fulfilled, starting in 1948. There is still a possibility that a future leader of Iraq will cause further problems for Israel, but it doesn't look like prophecy requires it.
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