The claim here is that under open borders, the skills of the immigrants may not match the skills that are needed by the economy receiving the immigrants. Thus, the immigrants may be unable to find gainful, productive employment and/or contribute meaningfully to the economy and society of their destination land. See also the high versus low skill.

Below is a quote from The New Case Against Immigration: Both Legal and Illegal by Mark Krikorian, where he makes this point:

In addition to native-born minorities, young workers, and others, a final group of people marginal to the economy is harmed by ongoing mass immigration into a modern economy: earlier immigrants. As management theorist Peter Drucker wrote, “Immigrants have a mismatch of skills: They are qualified for yesterday’s jobs, which are the kinds of jobs that are going away.”22 Over the entire course of this new wave of immigration that started in the 1960s, the immigrant population has been doing steadily worse relative to Americans; in other words, although immigrants increase their earnings during their time in the United States, the gap between their earnings and those of the native born has been steadily growing for decades. For instance, while immigrant men earned slightly more than their native-born counterparts in 1960, by 1998 they earned fully one quarter less.23 Another way to look at this is to note that in 1970, the percentage of immigrants and native born who lived in or near poverty (double the official poverty level or less) was the same, at about 35 percent. The mismatch between immigrant skills and the needs of a modern economy has caused a gap to develop and grow steadily, until in 2005, when the total of the poor and near-poor among Americans had fallen to 29 percent, the poor and near-poor accounted for fully 45 percent of the immigrant population.24 Of course, maybe the widespread poverty we see in the immigrant population is just a statistical illusion; that is, maybe because there are lots of recent immigrants (who are unfamiliar with America and know little English), they skew the averages and make the trends look bad even for long-term immigrants. If this were true, then the trends for long-term immigrants would be different. But they’re not. We can see this by comparing the native born to established immigrants, those here between ten and twenty years, thus long enough to learn the ropes in their new country, but not so long that they’d be retired and earning less. Such a comparison shows a steady deterioration in the position of these established immigrants, both in the proportion living in poverty or near-poverty and in the proportion owning their homes.25 In other words, each successive group of immigrants, even after decades of living here, is falling further and further behind the American mainstream. George Borjas found the same thing when looking at successive groups of young male immigrants and how each did over time.26 Those who arrived in the late 1950s started somewhat behind their American counterparts, but by 1970 actually had higher incomes. The group that came in the late 1960s started somewhat further behind the American average (partly because the American average had by then increased), and made slower progress, never quite catching up. Those who arrived in the late 1970s started even further behind the native born, and closed some of the gap, but not as much as those who came before them. And those who came in the late 1980s not only started even further behind the native born than their predecessors, but they didn’t catch up at all during the 1990s, instead seeing the gap between their incomes and those of the mainstream get even wider. As Borjas puts it, “the waves of immigrants who made up the Second Great Migration had lower starting wages and lower rates of economic assimilation.”27 The story of immigrant economic progress doesn’t end with the immigrants themselves, of course; perhaps the more important question is whether the descendants of the original immigrants do better over time and catch up with the mainstream. Here, too, the mismatch between mass immigration and modern society is making itself felt. Borjas has found that the children of immigrants (the second generation) tend to advance their economic standing relative to the mainstream (Americans of the third generation and later) by five or ten percentage points.28 The problem is that as each successive group of immigrants is more and more out of sync with the needs of a dynamic modern economy, they are starting life in America further behind the mainstream—so their children, although doing better than their parents, are doing less well in relation to the rest of America. Borjas found that the typical second-generation man in 1940 earned about 18 percent more than other native-born workers; that advantage shrank to about 15 percent among the second generation working in 1970, and to 6 percent in 2000. This evidence of a growing mismatch bodes ill for the children of today’s immigrants, since the wages of the immigrant parents in 2000 were some 20 percent behind the mainstream. If the pattern holds, then the children of today’s immigrants will never catch up, still having in the year 2030 incomes 10 to 15 percent below the average for other native-born Americans.

Krikorian, Mark (2008-07-03). The New Case Against Immigration: Both Legal and Illegal (pp. 143-145). Penguin Group. Kindle Edition.