The best they can hope for is being pardoned for Illegal Entry (either bypass INS or overstaying their visa) - but to have a clean record, they must leave. For if they’re still in this country the next day, they are still subject to deportation as they are continuing to commit a crime (which is being here illegally).
They also have to be named on the pardon - individually - to be pardoned. You don’t pardon a group or class. You pardon a person. “Person” is a legal term.