Japan and China are sociodemographically in dire straights due to a lack of birth and immigrant infusion. Indeed, a healthy percentage of gross domestic product increase in the United States is directly attributable to the work and earnings generated by current immigration. While lawful entry is still a critical policy, for those immigrants that have come to the United States, gained a legal foothold by working, paying taxes and obeying laws, then an amnesty program whereby such individuals pay a healthy fee, take amnesty exams and otherwise demonstrate an ability to stay in the United States as positive contributors to the society is a mutually beneficial construct.
The fee paid would be in excess of any social program drain the immigrant class would impose as also measured by tax revenues received. The key is that the immigrant seeking amnesty would need to be a net financial benefit to the United States. If so, then having the immigrant remain in the United States is an absolute positive economically and sociodemographically.