Beyond the grim shuffle of the unemployment line looms another specter in Smokestack America: the growing number of those who have exhausted their tenure in the great safety net of unemployment insurance and still can find no work.

The number of Americans filing for their last few weeks of emergency benefits nationwide more than tripled in two months, to nearly 1 million in the week ended Nov. 13, and is still rising, according to government figures. As workers let go in 1982's major plant closings and layoffs run out of benefits, they are expected in coming weeks and months to swell the ranks of those known in bureaucratic tabulations as "exhaustees."

As Congress left home for the holidays it approved legislation providing up to six weeks of additional benefits in some jurisdictions. But that is only a palliative.

Of 12 million Americans counted as jobless, only about 5 million -- fewer than half -- are now collecting unemployment benefits. Many of the other 7 million were never eligible for benefits; they were not covered by the federal-state insurance program. But large numbers also have gone through the program, and now come out the other end.

Rep. Joseph M. Gaydos (D-Pa.) spoke recently of a mass expiration of benefits as "the bottom of the pit . . . . Then things really will begin falling apart."

Already, in the Baltimore area, 58 percent of the laid-off steel and autoworkers -- nearly 4,000 -- were due to exhaust all their benefits a week before Christmas. In Ohio, some 54,000 of the unemployed were on the verge of joining the exhaustees. In Michigan, 100,000 have run out.

The dilemma posed by the long-term unemployed has been an issue in the nation's politics at every level this autumn and winter. Congress and the administration fought over jobs programs in the lame-duck session. The president prevailed and no programs were enacted beyond the extension of unemployment compensation in some states and the highway repair program to be financed by an extra tax of a nickel a gallon on gasoline.

In Michigan Thursday, Gov. William G. Milliken proclaimed a "human emergency" and called for a specially funded program to provide food and shelter for the needy.

At the same time in Pennsylvania, however, Gov. Richard L. Thornburgh's administration was cutting welfare benefits for all able-bodied, "employable" citizens. Dubbed "Thornfare" by outraged labor leaders and other critics, the action affects an estimated 97,000 recipients.

Nationwide, the surge in the numbers of "exhaustees" is likely to overtake social services already strained beyond their limits because of cutbacks in funding.

"It's like living in an empty room," said Denise Brzezinski of Vandergrift, whose husband Alan, a skilled overhead-crane operator once employed by Allegheny Ludlum Steel Corp., has been out of benefits for over a year and out of work since 1980. They have two small daughters. She wrote a letter to the White House last spring and in response got a phone call from a Reagan aide, promising to help her husband find work. The aide had no luck either.

"I used to be against the criminal on the street," said David Carman of McKeesport, a laid-off steelworker and father of six young children, whose benefits will soon run out. "But now I see what he sees . . . I got six mouths to feed."

Without the safety net, these families are forced to somehow weave their own, like Alexander the Great's spider, swinging precariously from day to day on strands of public and private help, odd jobs and creative barter. Their world can turn on a box of laundry detergent or a handout from Uncle Wilbur.

Many, like steelworker John Linkes, tell of making the painful leap from insurance benefits to charity, of learning to take help from relatives they thought they'd grown independent of, of trying to decide whether it's worth signing away their car and letting officials put a lien on their home so they can get on welfare.

Sheriff's-sales foreclosures have doubled in the Pittsburgh area since 1979. But, while some families have lost their homes, many are still coasting on the reserve of their former lives; since they were hardworking and thrifty, they own too many possessions to be eligible for certain kinds of government assistance.

Linkes, 31, is a stocky, able-bodied man who, his employed friends say, will do just about anything to find work and feed his family. But he finds himself cast onto an economic junk heap. A laid-off steel mill laborer from West Leechburg, Linkes ran out of insurance compensation in September.

A few days ago, after he and his family were interviewed for this story, he called, elated, to say he had found a part-time job as a security guard at a local store, for 20 hours and $70 a week, 6 a.m. to 10 a.m. The work was to last at least through the holiday season. But after that he was unsure again.

Here is how life was for Linkes, his wife and three sons, before he found his job, and how it is quite likely to become again next year:

His wife was working, at least through the holidays, 20 hours a week at a nearby K mart for $70 a week, while he stayed home all day with their sons. Federal food stamps, plus a program that allots milk and cheese for women and infant children, provided about $230 a month worth of food, he said.

Linkes' mother and other relatives helped out from time to time with what they could. Linkes had to sell his life insurance policy. A friend gave him a deer he had shot, good for five or six meals. Another friend anonymously sent him a $15 food certificate.

At Thanksgiving, an uncle and his wife's employer each gave the family a turkey. Another time, a United Steelworkers' union food bank gave him a bag of groceries. The older boys get a subsidized lunch at school.

The family lives in a neat white frame house in a subdivision on a ridge; a faded flag decal that says "I'm proud to be an American" is next to the porch door. The bank had let his mortgage payments slide, allowing him to pay whatever he could, he said. But he was not sure he could keep making even minimal payments.

Linkes was also falling behind in paying his mushrooming utility bills. But, he says, "I found out that if you have a baby, they can't shut you off" (the youngest Linkes child is 18 months old). Linkes has applied for energy assistance under a program that would give him extra money once a year.

"I know all these programs. I ought to be a social worker," he said wryly.

"The relatives, they say, 'Can we do anything, anything at all?' . . . So I tell 'em what we really need is soap detergent, you know, to wash the kids' clothes. So they come with that."

He says he hates taking charity, hates taking help from his family, hates the fact that his wife has to work when she wants to be home with the kids, feels bad because he gets testy with others.

The world of the exhaustees seems to be filled with unnervingly mature and serious youngsters.

As Linkes cooked the precious deer meat one recent evening, filling the house with rich aroma, his eldest son, Michael, 15, spoke levelly about his career intentions.

"I'm going to be a chef," he said. "I figure people will always have to eat."

Linkes, who had been critical of welfare, finally swallowed his pride and applied for it but, he said, was ruled ineligible. He owns a 1980 American Motors Eagle, which, officials said, put him over the limit. But if he sells his car -- which he is refinancing -- he said, "How would I look for work, or get to it?"

Many exhaustees, like the Linkeses, cannot or will not move from the communities where they have spent their lives, even though the economy has trashed the jobs they used to do there -- in many cases forever -- and there are few other jobs available.

Many proud people, who once saw themselves as the backbone of America, now try to hide their struggles, according to union officials, social workers and others.

Yet, in the trajectory of the unemployed, the point at which they run out of benefits is probably the most stressful, some specialists say--the event most likely to produce divorce, wife-battering, child abuse and other effects of frustration and anger. All the problems associated with unemployment are compounded.

Some also exhibit, as one specialist put it, "amazing stamina."

Many speak about their plight reluctantly, and only because they believe it might somehow help their families. Some cannot speak about their situations without a continuous, throaty quaver of the voice, of which they do not seem aware. They often talk about how much better off they are than many others.

Many apparently are forgoing medical treatment for themselves, if not for their children. Doctors' visits in hard-hit Detroit, for example, are down by one-third.

"We can't go out for football," said David Carman's son Shawn, 13. He works a paper route and, along with his big brother, David Jr., 14, has a second job as a pin-setter in a bowling alley, to help the family of eight get along.

"I just can't let 'em play," said their father, who lost his job as a raw-materials stocker in a McKeesport steelworks. "I got no medical. Shawn already got hurt once before my Blue Cross ran out."

Carman senior recently got a part-time, no-benefits job as a janitor for the school district, he said, but was let go after a short time and replaced with a youngster not so likely to quit and go back to a higher-paying job in a steel mill.

This is a common problem, officials said. Employers in communities where there are concentrations of workers laid off from high-paying but declining basic industries, such as steel and autos, are reluctant to hire those workers for fear they may still be called back to the plants, where they would make three or four times as much money.

Unemployment compensation, nonexistent until after the Great Depression, has enabled people to maintain substantial incomes -- in some states, nearly as much as when they were working--for a certain period while they look for work. Some critics, including Reagan administration officials, argue that the program is too generous, encourages joblessness, and that once benefits expire most people return to work.

Clearly that is academic in some regions. The stories are familiar by now, from California to Connecticut, of lines forming long and early for even the most menial, low-paying jobs advertised.

Some exhaustees are able to make grim jokes about the Reagan administration's short-lived notion of taxing benefit payments. They are off the president's "screen," as one put it, and he can't get at them now.

Rep. Harold E. Ford (D-Tenn.), chairman of the House subcommittee on public assistance and unemployment compensation, and others have proposed extension of emergency unemployment benefits. But, an aide said, everybody realizes that can't go on. "We know an alternative approach has to be found for the long term."

Meanwhile, the patchwork of helping hands struggles to keep going past a burst of holiday generosity. Leon Lynch, a United Steelworkers official who is coordinating the union's food-bank program, sees his staff of grievance experts turning into social workers and fund-raisers. They see these unemployed people, he said, as "a perpetual social responsibility." CAPTION: Pictures 1 and 2, Alan and Denise Brzezincki, with family, ran out of benefits a year ago; the Linkeses recently were relying on $70-a-week part-time jobs and aid programs. AP photos