"Immigrants" are almost never a net positive for the natives. However, many times the culture of the natives is in collapse anyway, which is why the invaders get in anyway.
The society forms afterwards is largely that of the invaders precisely because the culture of the natives had already devolved to the point where they couldn't keep the invaders out.
The immigrants wiped out the natives in Texas when their technology advanced beyond the natives’. Sam Colt was responsible. But it took many decades and fighting and slaughter on both sides. The immigrants earned their spoils. New immigrants just freeload.