Illegal aliens have been hiding here for sooo many many years now that the only way the INS takes care of that problem is by way of Amnesty--which interestingly enough, usually happens before an election. As long as you don't commit a crime, your presence as an illegal will be unnoticed. After 9/11 the INS supposedly have stricter rules and regulations with regards to granting visas. Still, it is not perfect. A tourist can overstay and have no worries of getting caught. The INS have no funds and manpower to track every single entry.

Housing? Many stay with relatives who are legal residents or rent rooms instead.
SSN? Get one for $75 in downtown L.A....$150 if you want a fake green card to go with that.
Once you possess these two forms of documentation, you are all set. Get a job, rent an apartment, buy a car. Eventually get married to an American citizen or wait for the next amnesty. Easy. Hundreds of thousands have done it this way.

How can you deport someone whose whereabouts you don't know? Whose identity has probably changed? A lot of planning and a lot of taxpayers dollars is what it will cost, if its even possible. It's not gonna happen.