Referring back to the definition offered in the OP

In the study of folklore, the folk process is the way folk material, especially stories, music, and other art, is transformed and re-adapted in the process of its transmission from person to person and from generation to generation.

Taking a broad view, especially noting the word 'stories', then I don't think it is dead. So for example, within families, accounts given of relatives (person to person and generation to generation); narratives relating to society (see Brexit for example)

Does this make sense?