Rentals in the near-future will be of higher cost until re-adjusted or if the demand goes much lower. Also, renting with a bankruptcy on the record could be challenging.
Not trying to patronize, but going underwater does not mean bankruptcy. The only way people are going bankrupt is if they can't afford their mortgage (e.g. they lose their jobs). The job market is extremely hot right now, so it's unlikely we'll have bankruptcies. Worst case scenario, homeowners contribute more to their loan than to house equity every month. Yeah, that kind of sucks, but still way better than renting or being homeless.