Alpine passes that used to be border crossings ... and those that have become so
A pass is defined by its location on a watershed. (LPE). This EPL is often an administrative boundary, and if it is a border between 2 states, the pass will have a "top-of-the-range" status of border pass ... and it will appear in both countries' catalogues.
This status may not be permanent, as treaties have shifted borders over the course of history.
Here are a few examples:
France and Italy :
With the Treaty of Turin (1860) and the attachment of the Duchy of Savoy and the County of Nice to France, several passes in our Alps ceased to be border passes (e.g. the Galibier and Bonette) and others became border passes (Mont-Cenis and Vescavo - but they would only be border passes until 1946 with the Treaty of Paris).

Austria and Italy :
In 1919, with the Treaty of Saint-Germain, the Trentin (Welsch-Tirol) and the South Tyrol (SüdTirol), called South Tyrol were ceded by Austria to Italy. (Provinces of Trento and Bolzano).
The Stelvio ceases to be a border crossing and the Brenner becomes one.

In red, the border between Italy and the Austro-Hungarian Empire (before the Treaty of Saint Germain)
Blue borders: Italy/Austria, Italy/Yugoslavia and Austria/Yugoslavia (after the treaty)
Further east, between Italy and Yugoslavia:
With the Treaty of Saint Germain en Laye (1919), the border was pushed back eastwards and several passes ceased to be border passes (e.g. Passo di Solarie), becoming border passes again in 1947 with the Treaty of Paris.
Others, such as Preval Vršič (or Passo di Moistrocca) only crossed the border between 1919 and 1947.

In red, the border before (left) and after (right) the Treaty of Saint Germain.
The article (on the Cyclotouristes Grenoblois website): " Alpine passes that used to be border crossings ... and those that have become so "A detailed review of the changes that have taken place along the Alpine arc since 1860.