Picked up this Morgan vise this weekend. My question is about the attachment on the chain. It's sized & shaped to fit over the jaw, there's a second chain as well but missing the attachment, assuming for the other jaw. What are these for? Is it a custom addition or did these vises come like this? I can't find another example like it. Any help appreciated, thanks!

Looks like an attempt by the end user to keep track of the soft jaws.

Jaw covers are pretty common.  What's the material for that?  From here, it looks like copper, a fairly common material among machinists.

Clever idea.

Oh, and congrats: nice vise.  I've got a similar Prentiss Bulldog vise, that came with the rare "really rusty" option.  I need to clean it up and put it on the bench.  Soon.  Sometime.  While I can still remember what a vise is for.

I would be willing to say leg17 is correct.