  This paper proves a general collapsing result for families of stratified
Riemannian metrics $\widehat{g}^\mu$ on a compact orbifold $E$, subject to
suitable limiting conditions on the metrics $\widehat{g}^\mu$ as $\mu \to
\infty$. The result is distinct from similar theorems in the literature since
it does not require bounds on curvature or injectivity radius of
$\left(E,\widehat{g}^\mu\right)$ and thus allows for Gromov-Hausdorff limits of
$\left(E,\widehat{g}^\mu\right)$ which have strictly lower dimension than $E$.
The paper also introduces and studies a new class of stratified fibrations
between orbifolds, termed weak submersions, and new classes of geometric
structures on orbifolds, termed stratified Riemannian metrics, stratified
Riemannian semi-metrics and stratified quasi-Finslerian structures, all of
which play a key role in the proof of the main theorem.
