Some give a fake SSN and they do pay into SS, just not under their name. who knows where that money goes, or if the employer ever really pays it. Same for income tax.
I don't have any valuable statistic (but I am real skeptical of statistics anyway), but I suspect a high number of illegals are working without a green card, without an actual SSN and I doubt the employers send in any imcome tax for them, because they are transparent. They are working under the table (and employers are happy, because they don't have to pay them minimum wage) or as day laborers. On Friday, when they get paid, they go to Western Union and send the vast majority of their pay back home.
Now I will grant you that there are exceptions, business owners and salaried workers, but despite what the liberals say, I don't think this is the majority.