People are going to mention Joseon Korea and Tokugawa Japan. In fact, two people (/u/Shawn_Spenstar and /u/Das_Orakel_vom_Berge) have already:

This isnt my subject of expertise but it seems like Japan under the Tokugawa shogunate would have been pretty close to what you referring to. Their foreign policy of the time was one in which no foreigner could enter the country and no citizen could leave the country under penalty of death. However they did still trade with foreigners like the Dutch East India Company so it definitely not a perfect parallel.

Now I am no expert on Tokugawa Japan, or any sort of Japan, either, but I do know Tokugawa Japan had extensive contacts with its various neighbors (besides the Dutch).

In Korea there was the Dongnae Japan House, a Japanese-inhabited outpost that was a locus of trade and interaction between the two countries. As a generalization, before the mid-18th century Korea sold ginseng and Chinese textiles and Japan sold silver, and after the mid-18th century Korea sold things like cow hide (as well as ginseng) and Japan began to sell copper a lot more. Things like samurai swords and Japanese maki spread among Koreans in the environs of the Japan House, and of course the Japanese islands of Tsushima, approximately between mainland Korea and the main islands of Japan, have many Korean cultural elements to this day.

The people of the tiny Kingdom of Ryukyu were thoroughly under the thumb of the Japanese, and of course there was trade between the Japanese and these southwestern cousins. The Ainu of the north were also increasingly falling under Japanese hegemony and rule, consequently with dramatic events such as Shakushain's War in the late 17th century.

China. Despite the idea that China and Japan were both secluded from the outside world, Qing China and Tokugawa Japan also had much trade going on between each other. I know really little about this trade (besides how it affected the Japan-Korea trade especially Korea's former position as middleman) but apparently a 1753 Chinese ship headed for Japan carried more than 12,000 books. So yeah, the trade wasn't tiny.

Korea was known as the Hermit Kingdom for a reason as well. North Korea currently conducts trade with several nations with its citizens themselves having little to no outside interaction, so Tokugawa Japan and Joeseon Korea are actually both very good parallels for what the question asks.

The Joseon government never in fact viewed itself as the head of an isolated state, so I always have the feeling that it's somewhat biased to call it a Hermit Kingdom and whatnot. Besides it's not necessarily true that the Joseon people had little to no outside interaction relative to other pre-modern, agricultural societies. From an elite perspective it's obviously not true, since there were annual missions to Beijing - more frequent missions than any other country was allowed. On a more private and mercantile level there was a lot of trade with China and rather less (but still more than a little) trade with Japan. Uiju, a fairly large town, appears to have depended almost entirely on the trade with China. The Japan House was probably a big part of the success of Dongnae. Sometimes Koreans were even allowed by Beijing to buy grain in the Jiangnan (the richest part of China).

The Northern Region of Korea: History, Identity, and Culture has a chapter on how northern Korea was affected by the trade with China, and there's Schottenhaumer et al's Trading Networks in Early Modern East Asia. For Japan/Korea Frontier Contact Between Choson Korea and Tokugawa Japan is a case study of the Japan House and a good book, for the Ainu see The Conquest of Ainu Lands: Ecology and Culture in Japanese Expansion, 1590-1800, for the Ryukyus I found Okinawa: The History of an Island People pretty good. For the Sino-Japanese trade, sorry, I have nothing besides some information that accompanies the Japan-Korea trade. Also To the Ends of Japan: Premodern Frontiers, Boundaries, and Interactions might be helpful, but I have just read reviews of that one.