Ms. Nielsen’s distinction, if you can call it that, was that in attempting to placate a president for whom no anti-immigrant measure is beyond the pale, she presided over a season of gratuitous, inept and ultimately futile cruelty. In the process, she bent the truth, sought to evade accountability and did incalculable damage to the prestige of the United States. It is a miserable record.

In wrenching thousands of blameless children away from their migrant parents, it is Ms. Nielsen and her deputies who failed to establish any system by which to track and ultimately reunify families they were so intent on sundering. The stain of that policy will long endure.

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On Friday, two days before Mr. Trump gave Ms. Nielsen her notice, the administration filed court documents aimed at cleaning up this mess. In light of evidence that agencies under her command may have broken up thousands more families than was previously understood — many of them before headlines about family separation seized the national agenda last summer — the government said it would take at least a year, and possibly two, to figure out which children, and how many, remain apart from their parents.

A further one- or two-year wait, after the year or more of separation those children have already endured, means an additional toll of psychological trauma. That’s the reality: emotionally wrecked toddlers, tweens and teens. Yet Ms. Nielsen’s pronouncements on this have been legalistic and evasive. There was no policy of family separation, she said — only a decision to refer migrant parents to prosecution. Of course, that was predictably and inevitably going to lead to family separations.

Mr. Trump, incensed at the surge of unaccompanied minors and families who have flooded the border in recent months, legally seeking asylum, now broadcasts his intention to get “tougher.” That was the word he used to justify his decision to withdraw the nomination of Ronald D. Vitiello, acting director of Immigration and Customs Enforcement, to run the agency, a constituent part of Homeland Security. No doubt he seeks a successor to Ms. Nielsen who will satisfy the same criterion, by pursuing policies unlikely to withstand legal and constitutional challenges.

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The real problem at America’s borders isn’t insufficient toughness. It’s a broken immigration system that Congress, entrenched in warring ideological camps, has been unwilling to fix. And it’s a president, convinced that hard-line immigration rhetoric and policies are key to his political brand, who is more intent on riling up his base than forging a workable solution.