Okay, that's more like it!

Unfortunately, the links only consider people as taxpayers. This means that, for instance, if you have very low taxes, everyone is worthless.

This clearly can't be right.

Instead, what you need to look at is what the immigrants contribute to the entire economy, not just the government economy.

This maybe isn't the best link, but it gives a sense of the scale of the contribution: https://research.newamericaneconomy.org/report/contributions-of-undocumented-immigrants-by-country/. And it's comparable to the costs in your article--seems like a net win, actually, if you extrapolate that 40% of the immigrants have about $90B spending power, which means that all of them together would have $250B--well over the $120B costs. Then you have to figure out how much of that $250B leaves the country or simply consumes resources without paying anyone else (e.g. when you eat food it's a net drain), and how much goes back into the economy...but it sure looks promising.

If they are a net positive, as seems likely, then they are a discount way to subsidize certain industries (e.g. farm labor)--that is, it's cheaper to do it by having illegal immigrants than by providing a direct subsidy.

Now, maybe such a subsidy is inadvisable, but it is still a net boost to the economy. Depending on how the labor is distributed, it will probably make things harder for some people (e.g. those who face more competition) and easier for others (e.g. those who buy, I don't know, cheaper strawberries). It may well be a regressive rather than a progressive change--that would need to be looked at carefully.

And of course it would be far better if they were legal immigrants rather than illegal ones; then we could better account for health care, social services, and so on. That would just make the benefit larger.

Finally, regarding retraining and education--having a highly-educated work force trained in the jobs that are in demand is a great benefit for any country. We should do that regardless of immigration. If we had a robust program in place to better facilitate this, then the negative impacts on citizens of new immigration (legal or not) would be lessened. Of course if there was too much immigration, all coping mechanisms would be overwhelmed. But I think we're pretty far from that already, given the relatively high levels of unemployment in places like Detroit where there are comparatively low levels of immigrants (~5% in California vs ~1% in Michigan--I couldn't quickly find stats on Detroit specifically).

So, in conclusion: (1) immigrants, even illegal ones, are a net positive to the economy; (2) allowing more immigration legally would allow us to gain the benefits and avoid some of the downsides; and (3) pressure on certain industries needs a robust solution anyway so we should solve it for everyone.