Many legal nonimmigrants do not have social security numbers either. Social Security only issues SSNs to citizens and non-citizens who are authorized to work. There are about 60 nonimmigrant visa types. Many can live here but cannot work. They need to bank. The IRS issues them individual taxpayer identification numbers (ITINIs) so they can bank, file tax returns, etc. Some illegal immigrants have obtained ITINs. The better solution is not to issue ITINs to illegal immigrants. Banks and other private businesses should not become immigration inspectors. They lack the training to identify illegal immigrants. The laws are really much more complicated than looking at a passport.