The article Right to Rent: Will the Obama Administration Finally Fix Housing? by Dean Baker explains the concept as follows:

The concept of “right to rent” has been floating around Washington for almost four years. Under this proposal, foreclosed homeowners would be allowed to remain in their house as renters, paying the market rent, for a substantial period of time (e.g. five years) following a foreclosure. While several bills have been introduced in Congress, President Obama may now have a new opportunity to take the lead on this issue.

I had no idea that such a proposal existed when I wrote my post Solution to The Housing Market Crash with a vaguely similar idea.