Underwater homeowners may get additional federal assistance for refinancing government-backed loans under a proposal being revived in the U.S. Senate.

Democratic Senators Robert Menendez of New Jersey and Barbara Boxer of California plan to introduce a bill as soon as this week that would expand the existing Home Affordable Refinancing Program by promising lenders they won’t be forced to absorb the loss on refinanced loans that default, according to a person with knowledge of the matter. The person asked not to be identified because the timing is not final.