BoneDynamics Pro  is a  blender addon that allows you to make bones react to physics.

Features:

*Tweak  one or multiple bones physics parameters on the fly *collision on the entire bone *Bones react to movement and collision. *Super easy to setup. *Ability to stretch bones. *Ability to make a bone chain. *Easy to tweak (it uses soft body under the hood). *Upcoming updates for free.

How to use:

Check my youtube page for instructions on how to use this properly : https://www.youtube.com/watch?v=b4qt2jOmu9Q&list=PLRUmha6ifE53xz6pL4gTV4Pyih7BhCSvM

There's also an official discord server where you can get tips and some help :

https://discord.gg/JaeVteJFZT

• In pose mode, select the bone(s) you want to apply physics to and hit Add bone Dynamics

• Press play and move the parent bone to see the result.

Tweaking the physics:

In Pose mode, select the bone or the bones you want to tweak, hit play, and change the parameters on the UI, Changes will reflect instantly.

Alternatively you can navigate to  a collection named BoneDynamics, you will find inside the objects that are connected to the bones, the objects have the same name as their respective bones, select the desired object and go to the phyiscs properties tab. You will find a soft body modifer that you can tweak to your liking 

Tips:

If you want to remove physics from a bone, select the bone in pose mode and hit Remove Bone Dynamics on the addon. It will clean up the bone, and the bone object

The checkbox "Allow Bone stretching" on the addon will allow the bone to stretch and contract.

For making a seamless animation you should shift the start of your animation by at least 20 frames, Example: your animation length is 100 frames, it should start at 20 and finish at 120. When you are done with the animation set the baking from 0 to 120 frames. This way you will give time to the physics to settle before the animation starts.