I'm nor sure I buy that. Yes illegal immigrants are outcasts but let's clarify something. They are seeking something on an unorthodox way.
Jesus valued honesty and uprightness even if he associated with the bottom tier of society.
* He mentions that his shepherds enter from the front gate, while thieves enter from the back gate (despite need, going about it ILLEGALLY is still wrong)
* He mentions in the Good Samaritan that the one who was a neighbour was not the priest or Levite (but was also not the thieves who mugged him) but the one who had mercy. Yet illegals have no mercy for those who have to work harder and pay more taxes because of their "land of opportunity". Yes, they suffer too, often being exploited into labor or sex trade.
* Jesus would forgive the sins of such people, but he wasn't a tax collector or sinner. He came to help them. To save them from their sins. In Nazareth,where everyone was like "isn't he Joseph's boy?" he was able to do very little because they had it all figured out. Jesus helped those who were aware of what was wrong with them (often leprosy) and confessed it to Jesus.
Jesus would be a poor person during COVID who "we ask that you mask" but he can't because he has a mask phobia, an undiagnosed (because he hasn't he hasn't gone to any doctors lately, because he can't afford insurance) respiratory ailment, or an allergy to a certain compound on the cloth they make for masks. Who cannot go into stores for food, who cannot get his driver's license updated, and who is starving. And who will not break any rules to make anyone afraid. Who has to wait at food banks to get anything at all. He might even be declared to have it, yet feel no different. In fact, let's also put those who in quarantine yet still have food and other needs to take care of. Since Jesus was declared sinful quite a bit, though he did his best to give mercy to others. (He would not however be among those protesting it by going in stores in defiance of rules, that again is going through the back gate).
But that too doesn't work, except for being "least of these" because we are assuming Jesus has means to help. What we're looking for is a sort of wounded healer, who doesn't cause trouble for others and tries to help, but is declared a criminal regardless.
I would amend your illegal immigrant to: Someone who works as a volunteer at the border mission providing food and clothing for these people (not those who try to ship people illegally across lines, but those who try to feed or comfort them, and are often mistreated by border officers).