Ethiopia is an interesting example, but not of scarcity. While my country's population grew by a mere 40% since 1950 (and has been stagnant the last few decades), Ethiopia's grew by 534%, and shows no signs of slowing: https://www.worldometers.info/world-population/ethiopia-popu...
Had we grown at their pace, we'd also be experiencing famines.
As for why they couldn't leave - you can ask their neighbors. The West is not the only destination.