MEXICO CITY — The young Mexican couple packed their possessions in boxes and garbage bags 20 years ago, locked them in a room of their half-built house in Mexico City and then migrated illegally to the United States with their 3-year-old daughter in search of work, taking only what they could carry.

The plan was to return a couple of years later, but instead they remained, undocumented, in New York City. The boxes and bags stayed where they had left them, their contents mostly forgotten: a family’s beacon of hope.

One recent morning, the daughter, Guadalupe Ambrosio, now 23, stood in front of the locked door of that room, the key in her hand. It was her first visit to Mexico since she had left when she was 3. She was about to open those boxes and bags for the first time since they had been stored, reconnecting with her interrupted childhood and closing a yawning circle for her family.

Ms. Ambrosio, an undergraduate at Borough of Manhattan Community College, was never sure she would have this chance. She, too, is undocumented. For most of her life, had she tried to visit Mexico, she would have been barred from re-entering the United States.