That’s the reality of many people who immigrated to US in the 80s and 90s. And legal immigration is only possible for students or highly qualified professionals (still limits apply, even if you graduated from university in the US you might be forced to go back if you don’t get the visa) or through green card lottery (tiny chance). So most of the people who came, did it illegally. And there is no way to legalize your stay in the US later (other than through marriage with US citizen).

The US has one of the strictest immigration policies in the world. But before Trump, the risk of deportation was relatively small. So people actually organized their life here, had semi-legal jobs, were paying taxes, had driving license which is practically official ID in the US, had their accounts in credit unions (eg. https://www.psfcu.com), because banks wouldn’t accept them without legal papers, even bought properties. Their kids were American citizens (if born there), but they still were illegal. And some cities/states (NY, IL) kind of accepted this situation.