Well, you really can’t.
Solid means not moving.
The badge moves at the end of the lanyard, therfore, you cannot use cloth to fake it.
If you were to make the plastic part move along (not solid), then it would also bend and twist like if it were cloth.
What you need to do is make a specific asset with a single bone chain that attaches to the mesh, the bone chain will probably just go like a tie, from the neck to the lanyard.
Then you add a proper Phat asset to it.
Then you use CCD or some other light weight cckid? Collider to simulate phsyics on the pendant.
Then you make the lanyard a cloth with a very low distance cloth paint which will better sell the motion of it looking someaht realistic…
And that’s probably the best you can hope for - which isnt much considering just how bad chaos physics is…