Someday, when the global language is no longer English but some other language, the new global language will still be full of fossilized English phrases, just as English today is full of fossilized French and Latin phrases.
There is absolutely nothing going on in the world to suggest that happen in the foreseeable future though. There is no competition, and it's inherently hard to change like any standard due to chicken-and-egg, so it tends to only happen when the entire world system is completely upheaved, to the point of the old world being a small part of the new world, and to a degree far greater than the possibilities of today. The stuff going on in the world today is mild comparatively.
In particular, politcal falls of the sponsoring empire don't directly lead to much change here, actually. Latin kept being the language used throughout Europe centuries after the Roman state was gone and buried in the west. Scholars were still writing in Latin in the 1600s. Within my parents' lifetime, Catholic mass was still said in Latin.
The world you are imagining could just as easily be one where Chinese and Arabs dominate, the US and UK are a joke, and yet the dominant coalition paradoxically speaks English at least for elite communication anyway.
Did you know the original Latin language came from a tribe called the Latins that were vanquished by the Romans?
Reading the history of English after the Norman Conquest might be instructive too. For centuries the common people spoke the language that had been spoken locally, while the elites spoke the language of the old conquerers.
Fundamentally, you underestimate the chicken and egg effects involved, and they happen on a time scale of generations because that's the time scale upon which people learn languages.
