This is an interesting example but I think it's not very really helpful in understanding Libertarianism.

First let me answer your question directly: in this example, Libland is undoubtedly screwed because Xia has a monopoly on the food supply. The people of Libland would not be able to cope with this situation and they'd most likely be overrun. Sure, there will be pockets or resistance with guerrillas doggedly fighting on for years or decades, but as a state, Libland would no longer exist.

Nevertheless, I think that the example isn't helpful because of two positions:

1) The unexplained reason why Xia can produce food so cheaply. 2) That it would be uneconomical for anyone other than Xia to produce food.

In the real-world, there would be a competitor for Xia to supply food. Even if Xia started off as the only supplier, someone would realise that they could enter the market supplying food that's a little cheaper, higher quality or just a little more different. The people of Libland, knowing the dangers of relying on only one source, would then also start purchasing from the competitor _in_addition_ to Xia.

I therefore think that your hypothetical scenario wouldn't exist outside of the 'thought laboratory'.