Apply Constraints (Remove, have Object stay in place)

Well, the Object’s own values are separate from the Object it’s slaved to.

For instance, I have it Constrained to an Armature Bone. And if I copy the Empty’s location, then remove the Constraint, and then paste its location…it just jumps way over to its own original position, which is where those figures are from. So its LocRotScale aren’t altered as its moving along the Constraint.

Is this what you meant?