Hi Kurt,
Excellent question.
I’ll have to do a video but to fix the broken library link it is essentially the same way.
However, DO NOT SAVE THE BROKEN FILE OVER THE TOP OF ITSELF.
That step is very important!!!haha
Here’s what you do. (in Blender 2.79, haven’t checked in 2.8 yet)
Open the broken file > Save As (increment the number. ie anim_02 becomes anim_03)
Then in the outliner, change it to show the data
Down the bottom there will be a broken library link.
Click in there and change the name or location of the rig.
Save over the newest version ( anim_03 or whatever you just recreated)
Then reload that file.
It should relink everything on opening it up again.
I don’t think I have encountered the problem with the mesh not working anymore, maybe you made it local or something? Don’t know sorry.