Years ago, I knew of some refugees (brothers) from a troubled Central American country. I don’t believe they were here legally and they worked “under the table” for a certain employer. I believe one of them got fed up enough with treatment from his employer to seek legal status. He contacted an immigration lawyer and I think eventually got himself a green card.
Those are the key words in your post. The immigration process has gotten much more difficult, particularly since 9/11.