What to do with soft chicken bones after making bone broth?
Worm bin.

Worms need calcium and sometimes they struggle to get enough.  People recommend eggshells in the worm bin for that reason.  You are not supposed to put meat in the worm bin (because of rats) but I think these bones are ok.  They will fall apart pretty quick.   

If you don't have a worm bin you could bury them in your garden.  I am told tomatoes like extra calcium in their soil.  Do an experiment and put them all by one tomato plant and see if that one is bigger.  If you have kids the right age, show them what you are doing and maybe they will make it into a science fair project for next year.