Animate dog character with soft body physics "jello" legs?

Question

I have a model of a dog character (unrigged) that i want to animate with legs that procedurally react to the keyframed animation of the torso. Essentially behaving like a marionette, with the main body being rigid, while the legs attached have soft body physics, only translating and rotating from the joint where the body and legs meet.
I have tried separating the mesh into the torso and the legs, doing some parenting and assigning soft body physics (i also tried rigid body) to the legs.
The issues I ran into:

• The legs being "ripped" from the main body. (see picture) I want the legs mesh to deform and stretch while still being attached to the vertexes of the main body.
• The legs not rotating from the starting point of the leg, rather just "floating" relative to the main body.

To be clear, I want the leg movement to be completely procedural. I only want to puppeteer the torso, which will pull the legs with it.
My goal is to make it look intentionally fake, as if an invisible hand was dragging the puppy model with jelly legs.

My crude attempt at demonstrating the desired effect:

Answer 1

If I want to combine soft body physics with an armature, I usually do it via a dynamic mesh deform:

Suzanne has an armature modifier followed by a dynamically-bound mesh deform modifier. The target of the mesh deform modifier is bone parented to an appropriate bone-- here, to Suzanne's ear bone-- and has soft body physics, with a goal group and the default goal strength set to 1.0. There is plenty you can do to further tweak the physics. The quality of the mesh deform can be increased by using a vertex group to limit it, or by creating an outer shell with full goal, to smoothly interpolate from physics-based deformation to no deformation.

An alternative here is to track the positions of soft-body vertices (or rigid body origins) with your armature. For example:

Here, I've marked vertices in the soft body with vertex groups that the armature uses for damped track and locked track constraints, so that the bone automatically follows what the physics does (to a certain extent). The soft body in this case is not bone parented to the ear bone, but to the ear bone's parent. This can be done with rigid body physics as easily as with soft body physics, by tracking the origins of rigid body objects instead of marked vertex groups.