In 1968 (end of May through mid-June, I think) my family - my parents, my 14-year-old self, and my three younger siblings - spent a bit over two weeks as tourists in Brezhnev's Soviet Union. As I have recounted elsewhere ( if not on BaptistLife.com), we started out from Yokohama, where we boarded a Soviet passenger ship, the Khabarovsk, and sailed to Nakhodka, a small port near Vladivostok. From there we took the train, much of it the fabled Trans-Siberian Railway, from Nakhodka to Helsinki, Finland, with overnight stops in Khabarovsk, Irkutsk, Moscow, and Leningrad.
1968 was a very strange year in which to be an unescorted American tourist family, especially one headed by a Baptist clergyman, in the USSR. It was the year of the Tet Offensive in Vietnam, and of the Prague Spring of the Dubček regime in Czechoslovakia, of the assassinations of Martin Luther King and of Bobby Kennedy (the latter while we were on the train in the Urals), and of massive student and leftist demonstrations against the De Gaulle regime in France.
One item which I failed to mention in my memoirs of the trip, probably because "undocumented aliens" hadn't become the powerful phrase it is now in the United States, was the fact that in each of the four Soviet cities where we spent a night or more, we became for at least a few hours undocumented aliens. We had US passports, of course, and the passports contained visas authorizing our presence in the Soviet Union. But the rules of engagement required that when we checked into our hotel we surrender our documents to the desk clerk. We were then free to wander around the town, usually but not necessarily guided by a tour guide from Intourist, the Soviet travel agency in charge of foreign tourists. But I recall my dad's expressing to my mom his concern about the fact that if something happened and we came to the attention of the police, or needed emergency assistance, we would not be able to prove that we had the right to even be in the country. And we spoke essentially no Russian, so without the presence and cooperation of the Intourist guide it would be very unlikely that we could explain to the authorities where our paperwork was. I'm not sure how much of a concern this was to my dad, but I do remember him mentioning it to Mommy in my hearing.
FWIW. Nothing happened to make an issue of the fact, but I do have a little experience with undocumented alien status that most of my fellow citizens have probably been deprived of. On the other hand...
Mrs. Haruo and I know a guy, a Tlingit/Haida Indian from Alaska, who was once deported to Mexico because he was working in a sweatshop in southern California that was raided by the INS (ICE) and he had nothing on him to prove he was American, so along with many of his coworkers who probably were "illegal aliens", he was sent South.
So be sure to be assiduous in carrying your passport with you at all times, all you purported "legals"!