KODIAK, Alaska >> The morning after more than 40,000 Coast Guard members missed their first paycheck, and the federal government’s shutdown stretched into its fourth week, Eleanor King placed an empty jar next to her diner’s cash register.

In scribbled black marker, a sign on the jar, written in all capital letters, read: Donation Coast Guard. By 9 a.m. Wednesday, nearly an hour before a rainy winter sunrise, the jar held $120 — money with which patrons were effectively buying meals for members of the maritime force.

While the shutdown has affected hundreds of thousands of federal workers across the United States, halting paychecks and furloughing those who have been deemed nonessential personnel, it has brought a particular chill to Kodiak, a small town of 6,300 on an isolated island in the Gulf of Alaska.

Roughly a quarter of the island’s population is either an employee or dependent family member of the Coast Guard, which has now had to scale back some of its operations in one of the world’s most dangerous waterways.

A high cost of living is common to communities in the Alaskan wilderness, but the Coast Guard contingent in Kodiak makes the town especially vulnerable to the drought in federal cash. Local businesses like King’s diner are losing money daily even while trying to help.

Kodiak’s predicament is a result of President Donald Trump’s political fight with Congress over $5.7 billion in funding for a border wall, forcing the government to shut down and leaving a series of agency budget bills unfinished. That included funding for the Department of Homeland Security, the parent agency of the Coast Guard.

“This impacts everyone,” King said. Like some of the other businesses in Kodiak, her diner is giving a 10 percent discount to Coast Guard members; the donations from her jar help pay for meals.

The Coast Guard is the only branch of the military that is part of an otherwise completely civilian agency. It was created to enforce maritime laws and conduct rescue operations at sea, but it can be ordered to protect the United States from foreign threats during war or conflicts.

That the Coast Guard is going without pay during the shutdown is “the first time in our nation’s history that service members in a U.S. armed force have not been paid during a lapse in government appropriations,” Adm. Karl Schultz, the Coast Guard commandant, said in a statement Tuesday.

If the shutdown continues, Coast Guard retirees will not be paid at the end of the month.

Jed Bergstrom, who runs a food bank at a Baptist mission community center in Kodiak, said a Coast Guard family showed up at his door the day after service members were supposed to be paid.

Residents are donating fish and game from their freezers to their neighbors. Big Al’s Take and Bake, another restaurant in the area, sent more than 30 pizzas to a food bank on the Coast Guard base. They quickly disappeared.

Alexandra’s Salon, a hair styling shop, is giving IOUs to clients instead of making them pay, and the Alutiiq museum, focused on the community’s native heritage, has waved its $7 entry free.

But eventually, said Mayor Patricia Branson, if the government does not reopen soon, the business owners and landlords will have to find a way to get paid.

“I think it’s important that the people in the faraway land D.C. understand what’s going on in a small town,” she said. “And how people are affected by all this nonsense.”

Legislation known as the Pay Our Coast Guard Act, which was introduced this month by a bipartisan group of lawmakers, has gained support in Congress in recent days. But its fate, at least in the short term, remains unclear.

Other organizations have raised funds to help Coast Guard families, including a $15 million donation from the USAA financial services company.

Flush with greenery and emerald water in the summer, while cold and wet in the winter, Kodiak is economically supported by the Coast Guard base, one of the largest in the United States. The town is also dependent on its fishing port, which often oscillates between being the second- and third-most prosperous in the country.

The fishing industry off Alaska’s coast rakes in more than $4 billion annually, according to the National Marine Fisheries Service. But with most of that service also closed, Kodiak’s primary economic driver might soon be in jeopardy.

For now, little has changed. The fishing season for pollock opened this week in the northern Pacific, and the Coast Guard moved a MH-60 Jayhawk helicopter and its Kodiak-based crew hundreds of miles to a small base in the Aleutian Islands to help, if need be, with search-and-rescue missions.

Still, the Coast Guard has had to stop some of its law enforcement missions in the Bering Sea and Gulf of Alaska. Some routine patrols have been halted, as has the practice, in at least some cases, of boarding fishing boats to ensure that crews are following maritime laws.

“Generally, activities have been scaled back if it doesn’t support life and property or the protection of national security,” said Lt. Brian Dykens, a Coast Guard spokesman.

Besides search and rescue, and unlike at air stations in the mainland United States, the Coast Guard missions in Alaska often include medically evacuating people from remote areas — as aircrews have done at least seven times since the shutdown began.

The Bering Sea is known for its hurricanelike weather and 50-foot waves in the winter. It has claimed the lives of dozens of fishermen in recent years.

Salt water, battering winds and constant strain ensure that Coast Guard aircraft need constant maintenance. The flights that are based in Kodiak are responsible for covering 4 million square miles of coastline and ocean.

But with hundreds of civilians on furlough, a backlog of repair requests is quickly accruing at the Coast Guard’s primary maintenance hub in North Carolina. Already, active-duty Coast Guard mechanics are filling in for their furloughed civilian colleagues at the Kodiak Air Station.

If the shutdown drags on, the ability of the force to initiate the most rudimentary search-and-rescue missions is at risk of being hampered, said one Coast Guard official who spoke on the condition of anonymity to discuss the effects of the shutdown. Some of the smaller Coast Guard air stations across the country could close.

Lt. Cmdr. Zachary Koehler is among the Coast Guard helicopter pilots in Kodiak who are not being paid as they undertake missions over the volatile Bering Sea. He and his wife, Beth, have a son and daughter, both 11, and run Grand Slam, a toy store the family opened in 2017. The store has lost 30 percent in sales this month compared with last January.

“In the first couple days, I think everyone thought this wasn’t going to continue,” Beth Koehler said. “So they kept spending like they usually do. And after that first weekend, it was amazing — it just stopped.”

“It hurts,” said Aimee Williams, who spent 12 years in the Coast Guard and is married to a C-130 pilot who is still in the service. “And it’s just going to keep getting worse here until it’s fixed.”

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