Empirical evidence suggests that many immigrants who initially plan to stay temporarily, eventually do not return to their country of origin. This unexpected staying suggests suboptimal integration among long-term migrants. We develop a theoretical framework in which migrants may misperceive their utility or wage prospects in the host country at arrival. Unaware of these misperceptions, they decide how much to integrate and save, incorrectly anticipating the effects of these actions on their location decision in the long term. We show that any migrant systematically underestimates their probability of staying if and only if their misperception involves specific forms of pessimism about the destination country relative to the country of origin, either in utility or in wage prospects. While present bias does not systematically lead to these forms of pessimism, biases such as projection bias, narrow bracketing, and misinference do and thus can explain unexpected staying. Using the German Socio-Economic Panel, we find that higher levels of pessimism about utility and wages at arrival are associated with unexpected staying in the long term.