Actually we have good laws on the books but they aren't enforced and they need a tiny bit of revision. If employer sanctions were given real teeth 10 years ago we wouldn't be in the mess we're in. A verifiable SS number database is cheap and easy and should have been compulsory for all employees to be verified against it. We could still do it today and at least 50% of illegals would self-deport.
They have enforced it strictly but only in the SW and mostly in rural areas. The ones who got past the border states have been left alone.