Genworth Financial Inc., the insurer weighing a breakup after steep losses on policies covering long- term medical care, is seeking buyers for a life and annuity unit, according to people familiar with the matter.

The firm is working with Goldman Sachs Group Inc. on a sale of Genworth Life and Annuity Insurance Co., or GLAIC, said the people, who asked not to be identified because the matter isn’t public.

Genworth will consider selling GLAIC in parts if it can’t find a buyer for the entire unit, two of the people said.

In a sale, GLAIC would fetch a discount to its year-end capital and surplus of about $2.1 billion, one person said. Capital and surplus represents the difference between the value of an insurer’s assets and liabilities.

Genworth rose 5.9 percent to $7.76 a share in New York trading Thursday, giving the company a market value of almost $3.9 billion.

Selling the unit could give Genworth the capital to buy back bonds and lower the company’s debt, according to David Havens, a credit strategist at Imperial Capital.

“The company is restructuring and responding to what’s an array of challenges coming out its long-term care business,” Havens said by telephone. “Probably a couple years down the road they could shift from defense to offense.”

Al Orendorff, a spokesman for Richmond, Virginia-based Genworth declined to comment, as did Leslie Shribman, a spokeswoman for Goldman Sachs.

Breakup Calls

Genworth announced a strategic review in February, after losing about $1.6 billion in the second half of 2014 because it didn’t have enough money set aside to cover payouts on long-term care policies, which help incapacitated people pay for nursing homes and health-care aides. It’s also selling a European unit that helps people pay bills if they can’t work.

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