There are more than a few options between politely asking them to leave and black bagging people off the streets by roving bands of masked, armed people with no identification
You (or the government) can ask a judge to order the civilian you don't like to leave. If the judge agrees, they have to leave. If the CYDL doesn't leave, you can ask a judge to order the police (or even you) to arrest and deport them. If the judge agrees, the police (or even you) can arrest and deport them.
If you don't have a judge's order to kidnap the person, then it's illegal by default.
It means you get deported rather than going to jail and you don’t get a public defender before being deported. There is no “due process” as in criminal law.
The concept of "illegal immigrant" is not a legal term and so it doesn't actually have any substantive meaning. One can accrue unlawful presence, one can be present with illegal status (when you do something your visa doesn't allow), but both of those are curable to varying degrees, the former subject to tolling (and also, doesn't count until one turns 18), the latter almost always because of the underfunded and overcomplicated bureaucratic morass that USCIS operates under.
But the common language of 'illegal immigrants" is exceedingly vague because it contradicts how the law its drawn up. One is not considered an immigrant legally until one has some sort of status that allows them to adjust their status to permanent residency. Before 1970 this was basically almost everybody. Today it's virtually nobody when they first enter the country. To be an immigrant is by definition to be legally present. The moral panic is actually based on a conflation between two distinct categories of people: those who entered the country without inspection (EWI) and those who are out of status and have yet to cure their status issue. Inspection doesn't literally mean what it means in the dictionary, by the way, it's a legal fiction. A wave-through is considered inspection even though one doesn't get their passport stamped. Parole can in some cases be considered the predicate that leads to inspection (advance parole establishes the inspection element that turns someone with no status into someone eligible for a green card) or it doesn't in other cases, although in those cases one is not legally considered to have been admitted into the country. Confused yet? Don't worry, DHS lawyers get confused over this as well, and even federal judges are frequently confused. Texas v. US was mooted but if it wasn't mooted, the petition actually reversed the terms of art which makes the petition gibberish if it reaches the merit stage.
Either way, whether someone is out of status or have status is not something that can be determined outside of a court and frequently, both administrative appeals and adjudication in actual Article III courts. ICE agents are not lawyers, they're not even technically cops, and they sure as hell can't tell the minutiae of immigration law where every word you think you know the definition of, you actually likely don't. One collateral attack that was commonly seen was that the person was actually a US citizen who never knew they were since depending on when you were born the criteria through which you acquire citizenship even while born overseas can differ dramatically. And by that I mean in the 1970s the criteria went under several changes that requires a whole new inquiry that requires some serious genealogical research to determine. This is a huge pain in the ass even if you know about the law, and ICE agents aren't lawyers and certainly aren't legal historians, but either way as a matter of statutory interpretation and application ICE agents making the determination would go far beyond what they're legally allowed to do. You and me and everyone else who aren't speaking for the government can use shorthands, but ICE agents can't while they're on the job. Who's "illegal" as a matter of law is not something ICE can actually decide, but they operate under presumptions that can't be rebutted since once they ship you out of the country, that's it. You can't get a visa to respond to a lawsuit. It used to be something that one can get parole for, but not anymore. Most no-shows in immigration court happen because of unavailability or because of lack of proper notice given. DHS OIG audits turn up this kind of problem all the time. I can believe that Trump and Miller having no clue about any of this, but the lawyers working for DHS? If they don't know, they're not competent for the position.
Interestingly native born Americans actually don't have a definitive and mandatorily accepted way to prove their citizenship. ICE routinely without evidence treat real documents as fake. You are not required to even have a state ID or driver's license, and neither is dispositive of status, and neither is a social security card. God forbid you were born at home with a midwife since many don't have birth certificates that conform to the more standardized forms of today. Most Americans don't have a passport. If you naturalize, at least the same agency will give you a certificate of citizenship that attest to your status. A green card likewise attests to your legal permanent residency status. But DHS doesn't issue such documents to native-born citizens, and routinely rejects documents issued by other agencies. ICE deports US citizens every year and we only have a limited set of data on how many. If you manage to make it back, you can't even sue ICE. You'd have to sue the municipality that held you for ICE based on what amounts to a hunch, which is not evidence. Voluntarily cooperating with ICE almost inevitably will lead to lawsuits, settlements, and once in a while, the bankruptcy of the city. Thanks to indemnity clauses, local cops are the last to get hit.
And all that is really unnecessary. The country was founded with open borders and while we had a lot of problems, immigration was not viewed as a problem serious enough for the federal government to specifically intervene in in the harshest and most racist way possible for 100 years. If you want both the economic benefits of immigration and also want immigrants to truly be seasonal workers voluntarily, get rid of the system and that will happen. Militarizing the border forced people into choosing which side they want to be on. I'm old enough to remember driving from Vermont to Montreal to hang out with my cousin at McGill for weekend brunches and smoked meats with just a driver's license - not even one issued in Vermont, but California - and the border checkpoint in New Hampshire - the only one in the state - being unstaffed most of the time. The southern border was like that until the 70s. Most Americans and Europeans don't have to contend with visas since visa waiver programs cover the so-called "First world nations" and some well-to-do ex-colonies and so the problem is an abstraction to them. In reality, it's a reality based on abstractions. Either way, since "illegal immigrants" are not a thing as a legally meaningful descriptor, there's no actual answer. Feel free to read this pretty good summation of the specific problems that involve the constitution though, it essentially covers up to Kerry v. Din (2015). https://scholars.law.unlv.edu/cgi/viewcontent.cgi?article=19...
