  In a previous work we proved the uniqueness and functoriality of primary
unfoldings on simple Thom-Mather spaces, which is a functor to the category of
smooth manifolds. In this article we extend these results for any stratified
Thom-Mather pseudomanifold with arbitary finite length, through a new kind of
intermediate desingularizations, the unbendings, which coincide with primary
unfoldings in the simple case.
