Is it possible to execute some action when the component is being removed / unregistered?

Hello,
what exactly do you mean by that?
Components are never unregistered or removed.

Even when the object it is attached to gets "destroyed"? Like when an entity / chunk / whatever is unloaded?

Very late but : you can use Quilt's or Fabric's standard library events for this.
I could add it as a feature to CCA, but it doesn't seem common enough to justify it really.