Can you mix classic cut out animation and deformation rigging?

I made a simple rigging of a character with parenting layers and then added a deformation rig so I could mix both techniques, but when I try to move the classic cut out animation, the deformation rig is left behind.

It’s there a way for the deformation rig to get stuck with the drawing? Or you just can’t mix both techniques unless you keep editing the rig while animating?

Yes you can. The deformation rig should move with your character if theres a peg above it moving it.