Mr. Banach said obstacles to using hospice services include a general lack of awareness and the stoicism of some veterans. “There’s a misconception about hospice that it means giving up,” he said. And this is a population that has found it difficult to ask for help. The V.A. hospice program aims to normalize the process and renew the vets’ faith in the system. In addition to care providers, there are veterans who volunteer to discuss shared experiences and “act as a gateway to accepting more help from more people,” Mr. Banach said.

Image The V.A. hospital in Ann Arbor, Mich., where Mr. Hellrung spent nine days in hospice care in June. Credit... Nick Hagen for The New York Times

At Vitas Healthcare based in Miami, Nancy Auster is a registered nurse who started her career serving in the Air Force 38 years ago. She serves as a liaison between vets and the V.A. who has helped veterans with challenges like retrieving lost medals. After telling a Vietnam veteran with no family, “Sir, we want to welcome you home,” she recalls he replied in a faint voice, “I’ve waited 48 years to hear this.”

Deborah Grassman, who has cared for 10,000 dying vets as a hospice nurse practitioner at the V.A. for 30 years and now runs Opus Peace, a nonprofit that provides educational materials for health care providers, originated the pinning ceremony that Mr. Hellrung experienced. She says, “honoring vets isn’t enough” and that hospice workers are trained to deal with the guilt and shame that many vets live with if they have killed people. “We help them unburden themselves and their family members,” creating “a safe emotional space where that stoic wall can come down and the pain can come forth.”

Courtney Butler, assistant vice president of hospice at Amedisys, a Baton Rouge-based company that is one of the nation’s largest hospice providers, said it takes a special set of communication skills to work with the many vets who have P.T.S.D. “You need to be careful in how you approach them so you don’t startle them. You shouldn’t stand over them to intimidate them.”

Since veterans often have fractured family situations, with few or any loved ones present at the end of their lives, hospice care can help them feel less lonely, said Dr. Sanjay Saint, chief of medicine for the V.A. Ann Arbor Healthcare System, where Mr. Hellrung was treated. He said that about 70 percent of his typical hospital patients had visitors, but only 10 percent of those at the V.A. did. “That’s another reason hospice care can be so comforting,” he said.

He recalled one veteran who was acutely ill but wanted to leave the hospital because he had no one to care for his dog. “That dog was his source of love,” Dr. Saint said. One of the staff members helped him contact a neighbor to feed the dog.

Ms. Hellrung continues to marvel at the way the V.A. hospice staff honored her husband after his service in an unpopular war. After his death on June 26, Mr. Hellrung was transported to the morgue in a coffin draped with the American flag. Everyone in the hallway saluted as “Taps” was played. “I knew my Timothy would have loved that,” Ms. Hellrung said. “He was a military man.”