A large amount of modern historical writing about Imperialism and Colonialism today dwells exactly on this subject. There are many historians who have set about highlighting the ways in which the Imperial project of the European powers were deeply influenced by native systems of rule and legitimacy. Imperial powers would absorb these systems, co-opt them and make them their own, but in the process were changed themselves. And in some cases the ideas born of these systems would then filter back to the mother country and reshape them at a fundamental level.

The example I will give here is of India. When the East India Company emerged as a power in India, it quickly faced problems of establishing its legitimacy. India was a large, complex country. What "right" did the East India Company have to act as rulers in it? They solved this problem by integrating into the existing system of Indian sovereignty, by seeking validation and authorization from existing "native" powers, such as the Mughal Emperor, or more regional rulers such as the Nawabs of Bengal and Arcot.

Now as part of this, and also partly driven by their desire to keep their own operational costs low, they thus set about trying to rule Indians by their own system of law. Thus, by the late 18th century, we see the British in India face the question of "what is Indian law" because they insisted that Indians were best ruled by their own law, and could not arbitrarily be ruled by English ones.

The implications of this was the idea of "native law" most notably the principle of Islamic law. To the Brits in India, Muslims were ruled by a certain set of islamic principles, and British judges and administrators were expected to continue with these principles. As the British expanded out of India into the Persian Gulf, Malaya, East Africa, they took this idea of native law with them. They would set about implementing these concepts, and in the process reshape the systems of law in each of these areas. In each British colony therefore law was something of a chimera, constituting pre-colonial systems, "native law" brought by the British, and English Law.

The impact of this sort of thinking reverberated back to Britain itself in some ways. Islamic Law was not a concept implemented in Britain, but there were institutional changes. The systems of law that the British devised in the colonies required clear lines of appeal. Thus, over time the judiciary in the colonies had to be brought under Supreme Courts and High Courts. These ideas would filter back to Britain itself, influencing their own judicial reforms in the 19th century which gave rise to the modern system we know today.

The East India Company's experiments in Imperialism also gave rise to a structured Civil Service, borne of the need to implement these various mixed principles. That Civil Service had a profound impact in shaping the modern British Civil Service that came to be.

So to answer, yes Empires were not just active forces but often reactive ones, and were deeply shaped by the native systems they encountered.

Some Sources that help explore this:

Bernard Cohn, Colonialism and Its Forms of Knowledge: The British in India (1996)

Bernard Cohn, An Anthropologist among the Historians

Thomas Metcalf, Ideologies of the Raj

Iza Hussin, The Politics of Islamic Law: Local Elites, Colonial Authority, and the Making of the Muslim State. 2008

Julia Stephens. Governing Islam: Law, Empire, and Secularism in Modern South Asia 2018

Elisabeth McMahon. Slavery and Emancipation in Islamic East Africa: From Honor to Respectability. 2013

H.V Bowen Business of Empire.