And when they match, as they will 99% of the time, is the employer then free to hire the illegal holding false documents? Will this employer still face penalties if it is later discovered that he has hired an illegal with false documents?
If only reality was as simple as your understanding of the issue.
There will be all kinds of other clues. Like the employer will find that they will have several employees that have the same SS number. We will fix these databases so it flags people who have several jobs in multiple states.
It will cost, but it's worth it. War is hell.
The Social Security Administration is getting in about $6 billion per year of withholdings where the name does not match the number. This has got to be from way more than 1% of illegals so your assertion is erroneous. My guess is that it is the majority. Most of them just make up a number and have no idea who it belongs to or if it has ever been issued or if it belongs to a child or a retiree or somebody long dead. I imagine you are right that some use valid social security numbers and matching names belonging to their legal relatives, acquaintances or perhaps their own anchor baby citizens.
I would absolutely give employers who followed the Basic Pilot Project process for verifying social security numbers safe harbor from prosecution if it later turned out that someone who had been verified was an illegal.
At the same time, I think employers who do not follow the Basic Pilot Project process should be held to a strict liability standard and that we should no longer accept their lame excuses about not being able to recognize obviously fake documents that wouldn't pass the laugh test for most of us at 20 feet.