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One in three migrant corpses remains unidentified, forcing investigators to send bone or blood samples out for DNA testing. Some bodies stay in coolers for more than a year.

Until the mid-2000s, unidentified remains were buried in Tucson. Now they are cremated to save money. Lockers at the center store the keepsakes of those who go unclaimed: a digital music player, $20 bills, paper with scribbled phone numbers.

With Martinez, investigators had a lot to go on: the personal belongings his family eventually would identify, including a business card for his dentist back in California. Examiners were able to obtain his dental records and make a positive match.

The Mexican government will pay to bring corpses home, but Martinez’s family scraped together $16,000 to bury him near their San Diego apartment, the living room walls lined with portraits of his mustachioed face.

“Here we go see him every weekend,” stepdaughter Gladys Dominguez said.

Mrs. Martinez, 43, speaks warmly of Mr. Jimenez for attempting to save her husband’s life. He settled in Fresno, Calif., after sneaking back across the borde, and said he wanted the widow to know her husband’s last words.

“He did all that he could,” she said. Now she hopes that the U.S. government finds a way to do more to prevent such deaths.

“People like my husband need immigration reform,” she said. “There are lots of people like him.”

Martinez was buried last May, on Ms. Dominguez’s 19th birthday. The gravestone bears a photo of him with his wife at their 2010 wedding and reads, “Juntos Por Siempre” — “Together Forever.”

• AP reporter Christopher Sherman in McAllen, Texas, contributed to this article.