CORRECTED - UPDATE 3-Triad unit winds down as Lightyear talks end

(Corrects to show Tonneson as CEO of Triad, not Lightyear in paragraph 5) (Adds Freddie Mac comment, paragraph 4)

By Al Yoon

NEW YORK, June 19 (Reuters) - Triad Guaranty Inc (TGIC.O), a mortgage insurer reeling from significant losses, on Thursday said its U.S. mortgage insurance unit will stop writing new business after the loss of a key customer and talks with a private equity firm ended.

Triad had been in negotiations for Lightyear Capital LLC and an investor group to provide up to $400 million in capital to form a new mortgage insurer.

The company also said Freddie Mac (FRE.N), the second-largest provider of funding for U.S. residential mortgages, declined to lift its suspension of Triad as an approved counterparty.

Freddie Mac will only buy mortgages with Triad insurance until July 15, a Freddie spokesman said.

Despite efforts by Lightyear to work with Triad, "certain hurdles arose that prevented the transaction from being feasible," Triad Chief Executive Officer Mark Tonneson said in the statement.

Triad will continue to seek alternatives with financial adviser Goldman Sachs Group Inc, but is not optimistic that it will find new opportunities, he said. Triad will trim about 100 jobs in the coming weeks as it begins the so-called run-off, during which it will pay legitimate claims on existing policies, Tonneson added.

Mortgage insurers, which bear some of the risk when borrowers finance more than 80 percent of their homes, have suffered as poor underwriting and falling house prices caused delinquencies to spike higher.