Ingrid Encalada Latorre, 33, spent the last six months living in a red brick Quaker meetinghouse in Denver, one of hundreds of religious communities in the United States offering refuge or other help to immigrants facing deportation. Supporters of these churches say they keep families together. Opponents say they harbor criminals at the expense of citizen parishioners who could use their aid.

Ms. Latorre came to the United States from Peru in 2000 at age 17. She took a nursing home job, and in 2010 authorities arrested her for using a Social Security number that belonged to someone else. She pleaded guilty to a felony, spent two and a half months in jail, completed four and a half years of probation and paid $11,500 in back taxes. Then, facing deportation, she sought refuge in the church in November. (Federal policy instructs officials to avoid arresting immigrants in places of worship.)

She has two children, both citizens. In the meetinghouse, she lived in an upstairs bedroom, exercised on a stationary bicycle and cooked in a kitchen by the pews. Her son Anibal, 1, learned to walk there. Her son Bryant, 8, adapted to new rules: As visitors came and went, he reached for a key on a wall, unlocking and relocking the door.