LAPEER, Mich. — A couple charged with second-degree murder after their two dogs fatally mauled a Michigan jogger agreed Friday to give up ownership of the animals and have them euthanized.

Valbona Lucaj and husband Sebastiano Quagliata signed the agreement with Lapeer County authorities on the same day they appeared in court on charges related to the death of Craig Sytsma, 46, of Livonia.

He was attacked by two cane corsos on July 23 in Metamora Township. The agreement says the dogs and a third cane corso will be killed as soon as possible.

The dogs have been in custody along with eight puppies. The puppies will be offered to an animal rescue group.

Meanwhile, bond was set at $500,000 each for Lucaj and Quagliata, although prosecutors wanted $1 million, saying they might flee the country. Magistrate Mike Delling settled on a lower amount but noted there’s “some question” about the couple’s status in the U.S.

It wasn’t immediately known if the couple could pay the bond and get out of jail or arrange payment through a bond agency.

“It’s a horrible tragedy ... but animal cases get a lot of attention,” assistant prosecutor Michael Hodges said.

He said an “extensive history” of previous attacks by the dogs had a role in the charges, which include possessing a dangerous animal causing death.

Lucaj, 44, a native of Albania, and Quagliata, 45, a native of Italy, have had a long-running legal battle with federal immigration officials after arriving here in the late 1990s.

Lucaj was named, but not charged, in a bribery scandal involving an immigration official in New York. The government said she and other immigrants paid a middleman to ensure they would be granted asylum.

The government in 2010 took some steps toward deporting Lucaj and Quagliata, but legal challenges have stalled the process, court records show. In March, a federal judge in Detroit declined to overturn a decision rejecting the couple’s application for naturalization.

Lucaj and Quagliata return to court Friday.