No, but once they are accused of doing illegal things they are afforded the same rights under the law as everyone else, no matter how they got here. At least that's my understanding.So people have a natural right to do illegal things?
Citizens do illegal things all the time. The Constitution doesn't protect them for prosecution either. But just doing something illegal doesn't make rights evaporate. In fact, many of the Constitutionally protected rights are in place specifically to provide certain legal protections to the accused.