Union workers in some financially strapped corners of American industry, who settled for less than they wanted in recent contract negotiations, now find themselves working for less than they settled for.

In an effort to keep their companies afloat -- and keep their jobs -- the unions are giving up part of their wage gains, cost-of-living benefits, favored work practices and other goodies.

A case in point is the United Rubber Workers local at Uniroyal Inc. In the spring of 1979 the union demanded a 40 percent pay raise over the life of a proposed three-year contract. After 19 negotiations and a 5 1/2-week strike, it settled for 27 percent -- a settlement that was roundly attacked by the Carter administration as a violation of the administration's voluntary wage guidelines.

But the union is making do with less -- a reduction of nearly 13 percent in its contract, for a savings of $50 million to Uniroyal.

The reason: Uniroyal made a persuasive case to the union last June that it had a choice: smaller paychecks or none at all.

The company was in trouble; it lost $120 million in 1979 and $12.1 million more in the first quarter this year. Over the last several years, Uniroyal, now the fourth of the Big Four tire makers, also lost about 22,000 workers.

"The company convinced us that it needed financial relief," said John Izzard, coordinator for the 1979 URW-Uniroyal talks. "So, being a responsible union, we sat down with them and worked something out."

More unions are finding it necessary to work something out with their financially strapped employers nowadays.

"It's happening all the time," said Kenneth E. Moffett, deputy director of the Federal Mediation and Conciliation Service. "It never used to be like this. I can remember the days when a labor leader would close a place down, rather than takes a step backward. But now many unions have to take that step in order to save jobs."

No one -- not the people on the Council on Wage and Price Stability, not those in the Bureau of Labor Statistics, not even Moffett, who spends much of his time in labor negotiations -- seems to know exactly how many unions are coughing up wage and benefit concessions.

"The unions don't like to talk about it. They always want to be publicized in terms of gains, not losses," a Bureau of Labor Statistics source said.

The companies don't like to talk about it either. Usually, a company seeking those kinds of concessions is having financial problems it prefers not to publicize," the source siad.

Because of the relative secrecy surrounding many of the negotiations, the concessions -- called "givebacks" by the employers and "takeaways" by the unions -- do not appear to be widespread, the source said. He added that there are no federal reporting procedures for concession agreements.

"But they're happening all over the place," insists Moffett, who added, "You have to be at the bargaining table to see it going on."

The most notable example this year involved the United Auto Workers and Chrysler Corp. In an attempt to steady the financially stumbling auto maker, the union reopened its three-year 1979 pact -- already contained $203 million in wage and benefit concessions -- gave back $243 million more.

AFL-CIO research director Rudolph Oswald called the UAW giveback "the largest in magnitude of any in previous years."

Other give back-takeaways are more subtle. For example, take the negotiations last May between baseball team owners and the Major League Players Association that almost ended in a strike.

According to Moffett, who was involved in the talks, the key issue involved an attempt by the owners to voir "free-agency rights" won by the players in their 1976 contract.

The players argued that the owners' move could prevent athletes from selling themselves to the highest bidder once they played out contracts with their respective teams. The owners countered that the free agent system dulls the competitive edge of teams losing "premium players."

As compensation, the owners wanted to have the right to take away decent, though not comparable, atheletes from the teams receiving the "premium players."

The matter is under study, Moffett said.

In New York City, which was tied up by an 11-day transit strike last April, a major takeaway move, from the view of the transit workers, is under way.

New York's Metropolitan Transit Authority has demanded that 31,000 members of Local 100 of the Transport Workers Union and 2,000 members of the Amalgamated Transit Union give back 20 minutes time off with pay, beginning Aug. 15.

Rand Burgner, an MTA spokesman, siad in an interview that the producitivity giveback could "help the authority realize $30 million in annual savings."

MTA faces an annual operating deficit of $255 mllion, Burgner said. He said the contract that the authority negotiated with the unions last April entitles MTA to the time cut in workers' lunch periods, coffee breaks and "wash-up time."

Union spokesmen, however, contend that the MTA has misunderstood the contract. Both they and Burgner agree that the matter is likely to go to arbitration.

Federal and private labor officials are eying warily the International Brotherhood of Teamsters -- the nation's largest union with an estimated 2.3 million members -- for the emergence of a potentially explosive takeaway-giveback case.

The Teamsters' 18-member executive board agreed July 10 to hear trucking industiry proposals for renegotiating the union's current three-year contract before it expires in 1982.

Under Article 27 of the National Master Freight Agreement that governs Teamster-trucking industry relations, management has the right to seek contract renegotiation in the event of war or any federal action that has "an adverse effect on the financial structure of the trucking industry."

Such an action occurred July 1 when President Carter signed a law deregulating trucking.

"The law means that many nonunion firms will be able to enter the field and complete against thse of us who ar unionized." said J. Curtis Counts, the president of Trucking Management Inc., the trucking industry's negotiating body.

The 1979-1982 Teamsters' contract provides wages of more than $11 an hour for unionzed truckers, coupled with a cost-of-living benefit that could tack on 58 cents an hour in October.

"Nonunion segments of the [trucking] industry don't have the same costs.That makes it much harder for the unionized segments to complete," Counts said.

Exactly what kind of relief the industry might seek is unknown at this point. The Teamsters, meanwhile, decline to say anything other than that the union "is engaged in purely exploratory talks," with the trucking representatives.

"To ask the Teamsters to come in and negotiate away benefits is a pretty tough thing to do," said another trucking industry source, who requested anonymity.

"They're not exactly known for giving up things. That's not how they got the reputation they have today. They aren't especially excited about the possibility" of having to make concessions, the source said.