Let us say that the siege here was 100 percent successful. One of the answers pointed out that even if it did, the country wouldn't just ... die. So we need a reason why, excluding:
- Religious reasons. In this part of the world where the war is, the religion is uniform.
- God-king or the like. The country is a type of constitutional republic, while still with lots of absolutism elements
My thoughts so far have been:
- Loss of an important trade center. If let's say, mercantilist politics are what keeps the country alive, the fall of the biggest trade center might be devastating, and the resistance would fall in a couple of weeks.
- Internal power struggles. Let's say that the emperor/king was in the city, and captured. Power struggles for what is left might make the country fall quickly.
What other reasons could there be?
The economical and technological level is late-medieval/renaissance, the city populates are 50% educated, while only 10% in villages. Still the news can be spread quite quickly, the fall would be known to everyone in a matter of days.