I create a dragon and I take care to have good topology, then add an armature to it, and did that by using the rigfiy addon, the problem appears when I move the torso widget in pose mode, the feet and hands don't move with it :
By default, Rigify's feet and hands are in IK mode. And the IK controllers have their parent set to "root".
To change that, you can either change from IK to FK, or change the parent from "root" to "torso" or anything you want. Note that all these properties are animatable.
For this, you need to select the IK hands/feet controller. Then in the sidebar, item tab, Rig Main Properties panel, you have buttons to switch from IF to FK, as well as change the "IK Parent"