It may be illegal, criminally or civilly, to enter into the united states without going through official channels, or it may be illegal, criminally or civilly, to remain in the country after expiration of temporary permission to be in the country. It is not, however, illegal to simply be an illegal immigrant, the crime is in the acting or failing to act, not in the status.

Generally it isn't that important a distinction, but it did come before the Supreme Court in terms of whether being addicted to drugs could constitute a crime. The Supreme Court held that one could be convicted of actually doing drugs (or possessing, distributing, manufacturing, etc.) but it was cruel and unusual to punish someone for being a drug addict.

This is, to be fair, a recurrent problem in adjudication with no simple answer - if the court spots a seemingly-winning argument not actually raised by any of the parties, should it pursue it or not? This is especially a problem when you have a judge like Richard Posner who (and this is meant to be descriptive rather than snarky) really is smarter than 99.9% of the lawyers who will appear in front of him (to an extent that may cancel out the countervailing fact that the lawyers will have typically devoted more hours to thinking about the specific case because they typically do not have as many other cases they also need to deal with at the same time as does a busy appellate judge), but may like all of us not always be able to spot all of the potential weak spots in his own ideas. The adversary system is not unlike peer review, even though those of us who participate in it for a living generally do not claim to be engaged in the disinterested search for truth. Here, I suppose since Judge Manion was dissenting he did have a chance (if he were so inclined or equipped) to take issue with the corpus evidence, but did not do so.

Imagine, in any event, that I arrive in the U.S. on a student visa, but fail to leave when I complete my studies. I would be in the country without currently-valid authorization, and would be subject to being deported. I would be an alien who "has come to, entered, or remains in the United States in violation of law" within the meaning of the statute Judge Posner was interpreting. I would be an "illegal alien," if you will. But I would have committed no crime.

To make something a crime you need a specific criminal statute which says that doing this particular thing shall be a crime, and what the penalties may be. Whereas a law makes lots of things illegal by specifying what is legal and ruling other possibilities out by implication.

For example, the law in my country requires that a landlord may only enter a tenant's home (even though it is their property) with adequate notice, explicit permission or in an emergency in order to prevent permanent damage (e.g. burst water pipes). But a landlord is not guilty of a crime if they, or their agents, break this law. Doing so is illegal, the tenant might be able to seek damages or a court order (and breaking the court order is _contempt_) but it is not itself a crime. If the tenant is present at the time, they could deal with the landlord like any other intruder, demanding they leave, using reasonable force to make them leave, or summoning a police officer. Again, the police officer won't arrest the landlord or agent, just force them to leave. If they become violent, _that_ is a crime and they might be arrested.

I'm not sure Judge Posner's reductios were a wise move from his point of view. They look like suggestions that some people might be eager to take.