Representativeness
More often than not, immigration flows are broadly representative of the population they originate from, but not always.
In the Irish potato famine, the poorest starved to death, those in trouble but with some assets bought passage to the US, comfortable people stayed home. Roughly speaking. The point being that the Irish moving to the US were not wildly unrepresentative - not just the dregs, not an elite either.
But in some cases, from some countries, those moving to a new country ARE wildly unrepresentative.
Since the qualities that tend to make people prosperous, or middle-class, or stony broke are somewhat heritable, a wildly unrepresentative emigration flow ( strongly selected) has long term consequences.