>>510075999 (OP)You can say "I don't consent to a search" all you want, but that only protects your ability to decline a requested search. If there is probable cause based on observed or evidenced crime in progress, then officers can search your property. They don't need a warrant to search your car or your person, if you're placed under arrest.
And so these cards and the information on them is only valid in the case that an officer of some description is approaching them at their home or in public, to try and ask them questions and coax an admission that they are illegally present in the country. But that's not really how ICE does things. ICE doesn't need to ask, they already know. When they raid a business or a house, they already know who's there and who they're arresting.
Also, illegal migrants do not get a lawyer. You are not being tried with a crime, you are being processed for expedited removal. You are not going before a judge, you are not innocent until proven guilty beyond a reasonable doubt, you are being removed. "Due process" is not a single universal thing. The process you are due, is removal.