In many poor countries with high emigration rates elderly people are left behind without care when their children migrate. Without a functioning market in private care migrants face a difficult trade-off between working their way out of poverty and providing informal care once their parents become frail or sick. I develop a non-cooperative model of siblings' interactions that explains how chain migration can lead to a breakdown of traditional caregiving structures while an opposing endogenous effect increases family members' incentives to specialize as caregiver. The model's predictions are tested using novel data from Moldova and found to perform better than predictions of some established migration models. The empirical analysis suggests that migration and staying in order to provide care are strategic complements for children of elderly parents in most families. This is evidence of a promising resilience of families' informal security arrangements to large-scale migration.