But there is some inherently ILLEGAL about it 
Perhaps “law breakers” would be a more accurate (or at least less controversial) term than “criminals”. Certainly no one can deny that illegal immigrants are breaking immigration laws.
This is the position in Australia. It is not lawful for a person without appropriate immigration status to be here, and if caught they will be removed, but they won’t have committed any infraction. It’s just not lawful for them to remain.
I don’t mean to dehumanise unlawful immigrants, but an illustrative analogy is perhaps to parking your car on someone else’s yard: it’s unlawful for your car to remain, but the car isn’t a criminal. The law here in Australia (and by the sound of it in the US also) makes a situation unlawful but does not impose a criminal sanction on the thing (person) involved.
Don’t bother criticizing this on the basis that a person isn’t a car, and should (unlike a car) be responsible for their own acts and be criminally sanctioned accordingly. I have no intention of buying into that debate. I simply raise the analogy by way of pointing out how it is.
You’re just not doing it right.
I dunno. They are in a situation in which they are liable to be deported. But somebody who, because of mental illness, is a danger to himself or others is liable to be involuntarily detained; there’s nothing inherently illegal about that, and he is not a “law breaker”. Similarly children lack, and in former times slaves lacked, certain rights and capacities, but without breaking any laws or doing anything illegal.
What we can say about illegal aliens is that they do not enjoy the right to remain in the US which is enjoyed by citizens, resident aliens and certain others. But I don’t know if there is a law explicitly requiring them to leave, in which case they break it by not leaving, or whether there is merely a law which gives the government the right to remove them, in which case I don’t see that they are necessarily breaking any law, or doing anything illegal, simply by not leaving.
PS: It’s worth noting that the US government may have good practical reasons for not criminalising the acts or status of illegal aliens, because it may want a deportation procedure in which they do not enjoy the constitutional rights they would enjoy if charged with an offence, or liable to be charged. So it wouldn’t be at all surprising to find that immigration law was deliberately structured that way.