President Barack Obama has an offer for many undocumented immigrants brought to the United States as children. Since Aug. 15, the Department of Homeland Security has been letting them apply for work papers and a deportation reprieve under a policy called Deferred Action for Childhood Arrivals. But the department says it had received fewer than 180,000 complete applications as of Oct. 10. That represents a small fraction of the 950,000 immigrants that, according to a Pew Hispanic Center estimate, could qualify immediately for the deferred action.

That got me wondering: What would keep people from applying? I’m hearing about immigrants having trouble gathering documents to prove their eligibility. I’m hearing about struggles to find affordable legal advice and scrape up the $465 application fee. But there’s another factor: fear. Many immigrants are wondering how long the policy will remain in place and whether the application information will be used for immigration enforcement. Some are also wondering whether they can count on the Obama administration, which has deported people in record numbers.

I found a pair of young roommates bound up in these questions. Both women have immigrant parents. Both grew up in Chicago. And both are college sophomores. But just one has papers to be in the United States. That woman, a U.S. citizen, wants to convince her undocumented roommate to take up Obama’s offer and send in the application. Their story revolves around trust, immigration status and who will have a future in the United States.