“Thou shalt not steal.”
One may not unilaterally appropriate to oneself what others own.
So, the grocery store has bread, I want/need bread, I may not walk into the store and help myself to a loaf or two, and then walk out without paying. That violates the commandment.
Thus, one may not illegally enter another country and “steal” the economic opportunity afforded legal residents of that country.
But in Catholic moral theology, at least, an exception is made if one is in dire need of the bread and legitimately has no other legal way of obtaining, and has asked the store manager or owner nicely for the bread one needs to feed oneself and one’s family (or has not had the opportunity to so ask), one may take the bread without payment, and it may be that no sin is committed.
So, too, with illegal immigration.
The illegal immigrant who comes to our country truly out of final desperation objectively breaks the law, but it may be that he does not sin.
Immigrants are obliged to respect with gratitude the material and spiritual heritage of the country that receives them, to obey its laws and to assist in carrying civic burdens.
And those laws include laws determining whether the person can be there in the first place.
He has certainly sinned, though his behavior upon ameliorating the immediate distress in which his family found itself would seem to determine the extent of that sin.
Of course, upon asking forgiveness for that sin, he would be commanded to sin no more.