One parasitic burden immigrants often impose is overconsumption.

Prosperity requires productivity. Productivity requires accumulated capital. Capital requires savings and investment.

When a people become prosperous on account of their propensity to save and invest, that attracts immigrants from less prosperous areas, with less prosperous qualities.

Even if they only consume what they produce, (that is, even absent redistribution and entitlements) they did not accumulate the capital which now enables them to produce. And if they do not save and invest at rates comparable to the natives, but consume all of their produce (or more) then they are not adding to the capital structure of their new home, but depreciating it, and eroding the conditions which temporarily allow them to enjoy higher incomes and standards of living than they formerly did.

Without those immigrants, the native people could retain exclusive use of that capital structure, and its full productive output, in the form of higher wages for their labor, while continuing to add to it.