Maureen, That's not just hypothetical!
Some toxins definitely do reside in adipose tissue.
The organic compound PCB accumulates there. My
professor who got his PhD on DDT was very cautious
about dieting off fat because it would be released into
bloodstream. Similarly mother's milk can have DDT
residues as the fat in the breast is released in
milk making.

In contrast, heavy metals are more likely to be found in bones,
and one of the probelme specualted for old age is that
osteoporosis may release them into the bloodstream also
(I forget the reference).

I think the word "DEtox" is all backward. As Steve
and others indicate, diarrhea, fever, etc. are signs the
toxic agent is present and active, not that it has left!