Minutes after Daniela Vargas spoke to the press in Jackson, Miss., on Wednedsay, the car in which she was riding slowed down and pulled over. Ms. Vargas, a 20-something who came to the United States from Argentina as a 7-year-old, had the day before seen immigration agents detain the rest of her family. As it turns out, she had been late in sending in a $495 renewal fee for the Obama-era program that allows some young undocumented immigrants like her to stay in the country – prompting her detention Wednesday.