According to family stories, my grandmother immigrated to the New World with an aunt, whose name I was grateful someone had remembered. Starting point!!!
She had lied about: Her name, Her age, her destination, her father's name.
But, she did survive the journey in 1905; to the boat in the old country. She got off the boat alive and disease-free ( unlike her brother-in-law, my great uncle who died a few years later of TB.)
Old age pension story- no papers -afraid to let the authorities know that she lied, fearing they would send her back to Russia