How did they get hired by Target to begin with?
EVERY person being employed is required by law to complete an I-9 form and provide ID documents. The employer is required to reveiw the documents prior to hiring the person.
And most companies have a basic background check run on the person whch validates (or invalidates) the documentation.
A few years ago I worked as a night stocker at Wal-Mart. NOBODY was hired unless they could prove legal residence. We had a few Mexicans and one Filipino girl. She was cramming for the citizenship exam. (The girl was asking me questions about this country I couldn't answer - embarrassing.)
When we bitched to the supervisor about being understaffed, she replied that 33 people had applied, four passed drug/background/immigration checks, two showed up and one quit the first day.