In this paper, we study consumption risk sharing when individual income shocks are persistent and not publicly observable, and individuals can default on contracts at the price of financial autarky. We find that, in contrast to a model where the only friction is limited enforcement, our model has observable implications that are similar to those of an Aiyagari (1994) self-insurance model and therefore broadly consistent with empirical observations. However, some of the implied effects of changes in policy or the economic environment are noticeably different in our model compared to self-insurance.