How do you know a person is an illegal alien without giving them due process? Also, every criminal can appeal rulings, that doesn't mean every criminal gets an appeal.
Being present in the USA is not an accusation of criminal activity.
Therefore if there is no record of them entering the USA legally and being here legally, its fair to assume they are not here legally and be deported.
Unless of course if the person can prove he/she actually IS here legally, which is where Due Process comes in.
Now, because detention and deportation for being here illegally is NOT a criminal matter, there is a worthwhile debate as to how much Due Process an illegal alien is entitled to. But yes, in general, if someone is here illegally and THEY believe they have a legal right to be here, they should be allowed to have their argument heard. How much appeal should they get, as this is not a criminal matter? Judges and lawyers gonna have to figure that out.
However I see no legal basis for deporting people to a foreign prison absent criminal conviction in the USA or in the country they are deported to. AFAIK the only country we should legally be able to deport someone to is their home country. And we should only deport them to a foreign country knowing they will be immediately imprisoned if their country has gone through the regular foreign criminal extradition process with a warrant.
None of that has occurred with Trump.
......and still, where do we keep all these people?
internment camps?
free on the streets with an ankle bracelet?
free on the streets with a temporary work card?
I think the best thing to do would be to give them a temporary work card so they can live and eat. If they are arrested and indicted for a crime, they go home immediately.