If you want to see the rest of this , take a look at what's happening in Russia now. They've sacrificed a ton of their low skilled labor, and cut off a lot of their migrant labor supply because of the terrorist attacks.
Wages are increasing, but the country is just about maxed in in productivity and looks to be at serious risk of collapsing.
Also, they're in serious trouble because even before the war they were not reproducing fast enough to replenish the labor supply, and immigration was supposed to account for that.
And, in general, the answer to your question is that more immigrant labor actually creates more and higher value jobs than are replaced by immigrant labor. Not just the services they need and want in exchange, but also the comparative advantage of non immigrant labor being able to focus on more valuable tasks.