Between Aachen and the Eifel a cycle path runs along an old railway line. Ride it and you change country several times without ever turning off. The embankment belongs to Belgium. The meadow beside it belongs to Germany.
The reason is one clause in the Treaty of Versailles. In 1919 Belgium received not only Eupen and Malmedy but also the Vennbahn, and specifically the line itself rather than the countryside around it. What became Belgian territory was the railway embankment plus a narrow strip on either side. Everything beyond that stayed German.
A line as territory: that stays inconspicuous as long as the line runs straight. The Vennbahn did not run straight. It followed the terrain, swung across German ground and back again, and wherever it did, it looped around parcels that nobody had negotiated over. Those parcels stayed German. They still lost their link to the rest of Germany, because Belgian soil now lay between them and the rest of the country. A railway line had turned into exclaves.
1919
Versailles awards Belgium Eupen and Malmedy along with the railway line.
1921
Belgium takes over the line. The embankment becomes Belgian territory, and six German exclaves appear.
1958
A section near Hemmeres returns to Germany. Six exclaves become five.
today
No trains left, but the border holds. On the cycle path you are standing in Belgium.
Belgium was given no territory, only a line. The rest followed from that.
— TerraTally · Borders desk
What that means day to day
The enclosed parcels are inhabited. People who live there live in Germany and reach the rest of Germany only by crossing Belgian ground, on a road that either crosses the embankment or follows it. The trip to their own local council leads over a state border and back again.
Inside the Schengen area this is barely noticeable. Before it, it was. Customs checks on the way to the next village, two legal systems for plots that touch each other, school routes and postal routes across the border: residents organised their daily lives around all of it for decades, long before guidebooks discovered the situation as a curiosity.
The administration follows the line too. Land registries keep it up to date, the municipalities on both sides know where their remit ends, and any work on the embankment starts with the question of who has to be asked. A border that looks like a slip of the pen on the map costs real work on the ground.
Rail traffic ended long ago; the legal situation stayed. The embankment now carries cyclists instead of freight cars, and it is still Belgian. It was corrected exactly once: in 1958 the section near Hemmeres went back to Germany, and six exclaves became five. The others stayed where they were.
The pattern matches other absurd borders. Nobody wanted these exclaves. They are the by-product of a decision with a different aim: the point was the railway, not the border. The border came along with it, and because it is in nobody's way today, it stays.