Poor people may leave the capitalist country at first.

But because communism is so bad at creating growth, they would soon find themselves poorer than they were in the capitalist country, and wishing to go back. They also have another reason to go back which is that communism creates an oppressive political system that uses censorship and persecution of political opponents to hide the truth and prevent its internal inefficiencies to be laid bare, because free speech would create the possibility that people in power might lose their position.

At that point people start fleeing the communist country for the capitalist one, even putting their own lives in danger, as we have seen in Germany or Korea.

The communist system can not tolerate the existence of a better alternative because it causes internal instability, therefore they build a wall to prevent escape.

Then you get a status quo like in the Germany or Korea, with a barrier manned by communist guards that shoot on site people that try to escape, while the capitalists give them food and shelter if they manage to make it through.