This is pretty close: 'anomie'.

According to Emile Durkheim:

"Under exceptional circumstances, when society is disturbed by abrupt transitions, it is incapable of regulating man's passions, it is then in a state of anomie."

Wolfgang Jilek, in studying the Coast Salish Indians off the coast of British Columbia and in studying other groups, has coined the term 'anomic depression', defined as such:

"This concept is introduced to denote 'an affective, psychophysiologic and behavioural syndrome developing in reaction to alienation from aboriginal culture under Westernizing influence.' The syndrome derives from experiences of anomie, relative deprivation and cultural identity confusion."

While these are sociological terms that carry with them deeper meanings in that context, this is the result of the process I am referring to.

I am wondering if there is a specific term for this process.

Please pardon my obsessive tendencies. Sometimes there is only one word that will do and you'll know it when you hear it.