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It's not just because of a larger population, it's also because illegal immigrants are often desperate, often willing to accept a much lower standard of living than locals, and therefore often willing to work for very low wages (sometimes illegally low)
Thus creating an under-class of workers who keep wages from ever going up to where they should be
The premise of the comment that you are responding to is that because of supply and demand, and because these people are desperate, it reducing the wages for those jobs and makes those bad jobs worse.
Thats horrible and less people should be doing those bad jobs, and the wages should increase! Desperate immigrants doing those jobs is just people pushing off bad things to a vulnerable population, and the world would be better off if those jobs got automated away entirely.