A friend of mine adopted her half-brother's kids from Israel. The INS idiots told her she'd have to have notarized paperwork from a US embassy--she's American, lives near DC. Duh.  Only if you are overseas do you need an embassy, for obvious reasons.  It took a Senator to straighten that out.

Then IRS wouldn't accept the paperwork to prove they were dependents. Yup, legally hers, couldn't be deported, but not recognized as either residents, citizens or dependents.

In our case, (1970s), the lawyer advised us to come in on a temp visa and apply for permanent. That was illegal at the time, since our intent was to be permanent. We had a house, jobs, visa expired, illegal (well, unvisaed) for three years until we could get a hearing, where we were able to convince the case worker our intent had not been criminal, and make our case.

We should have come on a boat from Cuba or Vietnam. Easy to get citizenship that way.

Oh, yes--old naturalization documents cannot be copied. USAF kept writing down my naturalization number and losing it. Took three years to get my security clearance, and meantime I was in the presence of stuff no one uncleared was even supposed to know existed.

Meanwhile I know an illegal alien from Canada--yes, there are illegal Canuckistani hosers invading--whose visa expired and has never fixed it.  He finally gave up on the system.

I know another Russian who came by way of the UK, got a work visa, had his company go bankrupt and disappear right after his transfer, leaving him here without income and no legal way to work to even get a ticket home, since the visa specified the job.  He eked by selling his books and clothes, until his mother (an American permanent resident) and a legal charity set up to help former Soviet/Russian Jews were able to wangle a student visa, with the requirement that he then had to find financing and schooling.

Did you know a large number of illegal Asians come in by ship to both the West Coast and NYC, and a number of them get tourist visas to Canada, then wetback across the longest undefended border on Earth?

Part of the problem is the rules change constantly, and interpretations vary by case worker, and every problem takes money and lawyers to fix.  I've never heard of anyone not managing without months or years of hassle for either residency or citizenship.