What are the chunks of connective tissue on soup bones? (And can I use them?)
What ever it is, sounds like sinew or other hard tissue, it's done it's purpose now the flavour, sugars, geletine etc is now in your broth and you should probably discard them. I don't imagine they will taste of anything now and the texture is likely to be vile.

By all means taste a bit to see what I mean. It won't make you ill though you may possibly gag...