So really, it's more like the woman merging with the kitsune-bi rather than being possessed by it? Since the woman's consciousness and memories are retained.
It's a traditional food for foxes. Purportedly they love the stuff. Interestingly, gaining an interest in fried tofu and certain other foods was believed to be symptom of what is known as kitsunetsuki which is almost assuredly what this profile was based on. So this is a case of the author showing their work more than anything else.