Three New York residents filed a federal lawsuit Tuesday against units of J.P. Morgan Chase & Co., alleging that the bank misled them about their chances of getting long-term reductions in mortgage payments.

The suit highlights one risk of the Obama administration’s effort to save millions of homeowners from foreclosure through loan modifications: The hope of receiving such relief may cause some borrowers to continue making payments, rather than accepting foreclosure and seeking more affordable housing. That could leave them in even worse financial condition after an eventual foreclosure.

The suit, filed in U.S. District Court for the eastern district of New York, says the three borrowers “relied on promises by [the bank] that they would be able to modify their loans so that they could avoid foreclosure” and so “invested their limited resources” in making payments.

A spokesman for J.P. Morgan said the bank would be “happy to talk with the customers, review their situations and see if we can help.”

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