Is it possible to create a rigid part that react to physics on a cloth object ?

For exemple in the following image i've put the right part of the mesh as fully pinned, and put a monkey head under the mesh. I'd like for the highlighted part to be rigid, not bend at all and keep its form.

I've tried to add springs or change the pinning values also touched the property weights, am i missing something or did i not change the values correctly, if possible ?