Post deformation

Is is possible to attach a null or an object to a point on a
grid that will move with the deformation of said grid?

Try object to cluser constraint.
You could also use surface deformation, but I assume you only intended to constrain it.

Hope this helps,
Urp

I should have been more explicit, I want to move with the
deformation caused by texture displacement. Sorry for the
ambiguity. But thanks for the quick help.

DB