It was supposed to be a regular visit home for Kun Suk San. The North Korean, who is employed as an operator of heavy machinery at a Soviet coal mine on the island of Sakhalin, had always spent his vacations with his family in Pyongyang, always taking canned food and other gifts along.

This time, however, Soviet customs officials became suspicious about certain cans stashed inside the Korean's suitcase. They opened a can of stewed chicken and discovered 26 Soviet-made wristwatches inside.

The Korean was detained and hauled to court at Uglegorsk, on Sakhalin Island in the Soviet Far East. Given the fact that he immediately admitted that he had been involved in illegal smuggling of watches, the court showed unusual leniency. He was sentenced to "corrective labor" of unspecified duration. This means, according to an account published in the newspaper Sovetskaya Rossiya, that Kun will be required to pay the Soviet state 20 percent of his monthly salary.

The court also decided to confiscate an unspecified number of watches found in his suitcase, an equivalent of about $650 found in his possession and the Korean's personal automobile, a new model of the Volga sedan. The car costs 15,000 rubles, or $21,000.

The unusual report glossed over the curious matter of what a North Korean citizen was doing in the Soviet Far East and why was he employed at a Soviet coal mine. Nor was it possible to discover from the North Korean Embassy here whether Kun was the lone North Korean employed at the coal mine or whether others also worked there.

Soviet authorities have become quite sensitive about the presence of workers here from other communist countries following recent reports in the West that thousands of Vietnamese workers have been sent here to work off Hanoi's debt to the Soviet Union.

There are also unspecified "thousands" of Bulgarian workers in the Soviet Union in what appears to be a trend within Comecon, the Soviet Bloc common market, to encourage the free flow of labor and capital among the socialist countries.

This trend appears designed to counter labor shortages in the Soviet Union while at the same time relieving the prospect of unemployment in certain less-developed socialist countries.

Another aspect of this policy, which has been in effect for several years, involves East European countries sending workers to help on projects for the development of Soviet natural resources. Several East European countries are currently participating in the construction of a major gas pipeline, although details about their role is regarded here as a state secret.

The Russians have been particularly incensed by reports in the West that planeloads of Vietnamese workers were shipped here to offset through their labor Hanoi's almost $3 billion debt to Moscow.

Responding to what it termed a campaign of falsehoods, the government newspaper Izvestia recently said that 7,000 Vietnamese between the ages of 17 and 35 have come here for "training" under an agreement signed with Vietnam a year ago.

The news agency Tass said the workers receive a three-month crash course in Russian, then spend nine months in vocational training, and are expected to work in the Soviet Union for four years. Their trip from home and the return journey are paid by Moscow. After three years they are entitled to a subsidized vacation trip home.

According to Izvestia, the Vietnamese workers are placed in the area "with the most suitable climate for them." It went on at great length maintaining that the Vietnamese were not like "guest workers" from southern Europe who are employed in the industrialized West European countries.

The Vietnamese enjoy the same rights as Soviet workers, get the same salaries and are given "well-appointed housing," the paper contended. Tass said they can remit "a part of their earnings" to their families in Vietnam. They are given free textbooks and other study material and their situation is entirely different from migrant workers in Western countries who are "oppressed" and who are denied equal rights, Tass said.

The Vietnamese workers reportedly are employed at chemical, machine-building and textile plants and land-reclamation and irrigation projects. Izvestia said their employment here is going to turn them into highly skilled workers and that this will serve "the interest of the economic advance" of Vietnam when they go home.

Another dispatch talked about "thousands" of Bulgarians cutting wood in the northern Komi Autonomous Republic with the Soviets providing machinery, housing and fuel. This project was described as "a new form of economic integration" with the Soviet Union and Bulgaria sharing the wood produced there. An unspecified number of Bulgarians also work at the Kursk steel plant.

Western diplomats here have speculated that the Soviet Union intends to increase the number of migrant workers in the future. The manpower shortages here have become a serious problem. According to official Soviet figures, there were 2 million job vacancies in Soviet industry last year.

Moreover, according to official Soviet estimates, about 700,000 new workers are required each year for the foreseeable future to keep existing and planned enterprises operating efficiently.

This requirement is particularly acute in the context of the Soviet demographic problem. The Soviet Union's rate of population growth has been falling since 1960, when it was more than twice the current level of 0.84 percent. What growth there is now is largely confined to the Moslem population of Soviet Central Asia. The growth rate of the country's European population is almost flat.