If they have no legal status then how are they illegal? If the laws don't apply to them, then how can they be criminals?
Also, the Constitution does not exempt non-citizens. Nor does it say it only applies to citizens. Throughout the document it says "Person."
Here's an example. The 5th Amendment: No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury, except in cases arising in the land or naval forces, or in the Militia, when in actual service in time of War or public danger; nor shall any person be subject for the same offence to be twice put in jeopardy of life or limb; nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation.
See how it says "no person" and NOT "no citizen"? Do you see how the Constitution says it applies to Every. Single. Person. and not just citizens?