I know that the Soviets built a wall around West Berlin to prevent people from east Berlin to escape. But, instead of trying to escape to west Berlin through the Berlin Wall which was very heavily guarded people could have tried to escape to mainland West Germany.
It would have been much easier since the border was longer and unlikely to be as heavily guarded plus they could just escape to some other country (like Denmark via sea or Chechia) and then make their way into west Germany.
Even if they want to SPECIFICALLY go to west Berlin I suppose west Germany was connected to west Berlin for the most part of the cold war.
Edit: spelling correction.
More can be written about it, but you might like to start with the answer by /u/kieslowskifan in "During the cold war, why did East Germans try to escape into West Berlin?" . For more details on the fortifications of the inner German border, you can see "Why did people try to defect over the wall in Berlin and not through some unguarded part of the huge border between East and West Germany?", with several answers by /u/Poebbel .
This is not to discourage discussion. Further questions, data, and debate are welcome.