An expanding menace culture will also be young, just because anything growing fast can't have been doing it for long. By comparison, a stable culture can stay that way indefinitely, spending its resources accumulating knowledge and skills instead of on expanding, and so can accumulate a very great deal of both over a vast stretch of time. It has perhaps less access to materials, but a solar system has a great deal of material to start with, and it is not stretched thin.
When an expanding menace tries to absorb the ancient stable culture, it has key disadvantages. Its attention is spread over activities on a large periphery, and its stores of knowledge and weaponry are limited. The ancient culture has been found by many menaces before, and survived them all. It knows of other old, stable societies, and they may even have evolved a common plan for dealing with menaces.
It is conceivable that the expanding menace would try to flow around the old stable societies, like a river around rocks, without threatening them enough to provoke a backlash, but that runs against the logic of expansion.
So, odds are any expanding menace will encounter one of them, or more than one, if needed, before it gets to us. Each such encounter will be an existential challenge at bad odds, which multiply out increasingly close to zero.
Thus, the stable condition of a galaxy is a sparsely occupied archipelago of deeply ancient, unassailable cultures not interested in expansion, so not visiting, e.g., us, with the occasional rash of menace, dealt with firmly.