No, but they don't serve prison terms either. Punishing the innocent is NOT the right thing to do. What is needed is a solution that correctly addresses both parts of the equation.
Children go back to Mexico and when the turn 18 they get a one time shot a citizenship including a real ssn and registering for the draft. If they wait too long, past their 19th birthday they forfeit any chance at head of the line immigration privileges. Just one of the pack,
If a man robs a bank and uses the money to buy a house for his kids, do the kids get to keep the house and live in it?
The "loot" in this case is residency which must be given up because it doesn't belong to them.
No, I don't think children should be prosecuted for their parent's crimes, just give up their ill-gotten gains: deportation.
To talk about how tough it will be for them is to engage in emotional blackmail. Their parents did this to them; we didn't