Since an international understanding of citizenship as a human right did not really cohere until after WWII, I’m going to focus this answer on what happened in Central/Eastern Europe in the first half of the twentieth century, which saw this kind of territorial reconfiguration happen multiple times over a few decades and two wars. (Assuming this is what you’re interestes in given you mentioned Germany and WWI)

Generally in short, people did change citizenship as borders shifted (or in earlier centuries, the monarch they were a subject of). There’s a famous partly apocryphal story of the woman who held five different passports in her life, but never moved from her hometown. This is paraphrased from Philippe Sands’s East West Street (incidentally a compelling read). The hometown he specifically writes about is today’s Lviv in Ukraine, which over the past century went from being offically Lemberg (Austrian Empire) -> Lwów (Poland) to several USSR/Nazi wartime occupations -> Lviv (USSR) -> Lviv (Ukraine). So officially, in terms of the passport they travelled under, or the laws they had to follow, this could change overnight.

What they were ‘considered’ is a different and more complex matter, especially in regions that had been heterogenous for many centuries, such as Bohemia, South Tyrol, Silesia, and Transylvania among others. To make matters more complex, the Habsburgs in the course of territorial expansion to the East and Southeast had encouraged the movement of many German (speaking) settlers, which is partly why small communities of German speakers still live in parts of SE Europe. And of course, the existence of Jewish, Roma and Sinti, and other minority communities also muddied the waters, so to speak.

As the ‘national idea’ coalesced in Europe in the 19th to 20th centuries, language and culture were usually what people used to identify what nationality someone was. This was difficult in areas like the above where many were of mixed families or just happened to be multilingual. When after Versailles new nation-states started to quarrel over certain lands and populations, people were often pressured to ‘pick a side’, a process Tara Zahra describes in her excellent book ‘Kidnapped Souls: National Indifference and the Battle for Children in the Bohemian Lands, 1900-1948’. Hitler also used the excuse of protecting German populations to justify expansionism towards the East, with devastating results I will not recount here. However this is relevant, because following WWII a large number of population transfers took place as borders were redrawn again - with millions of Germans being expelled from their homes in what was now Poland and Czechoslovakia, for example, sometimes marched across the nearest border. A great book on this is RM Douglas’s ‘Orderly and Humane: The Expulsion of the Germans After the Second World War’.

Legally prior to Nazi invasion such people would have carried Polish or Czechoslovak citizenship, for example, but were probably seen as German. Given many collaborated or were at least registered as German under occupation, these people were later identified and driven out of the postwar Polish/Czechoslovak states. Central and Eastern Europe today is far much more homogenous than it was a hundred years ago because the international standard of a majority nation-state has been normalised, something that is a relatively new phenomenon and that has come out of recent historical events.

Sorry to ramble, OP, but I hope that answered your question in a roundabout way - the books I mention are really excellent both as case studies of the overall topic and also cite more general works and articles. Corrections are welcome!