Weird way to say it, instead of program say PC and see if the answer changes.

The program puts glibc in a context to implement business logic, detached from this context glibc can't be used for anything.

Exactly - it’s still there (and still has its own semantics), but it’s also inert.

And, to address your point directly, of course mathematics detached from context can be used in practice. One can certainly create-slash-discover an abstract algebra, derives theorems about it detached from outside context, and then later on discover a context in which the abstract structure is applicable, and apply the pre-derived theorems.