Here's a little blog to help other folks who have had this happen to their resin dolls, and what I did to rectify the problem.
My Sybarite's head broke where the little resin hook inside the cap held the elastic cord . You can see it on the head cap on the right in the pic below.
I went to my local hardware store and purchased an S hook that was larger than the neck hole.
I tied a piece of ribbon onto the elastic cord (because once I remove that little broken hook piece the cord will snap back into the body. We don't want that to happen!)
You can see here that I am pulling up on the ribbon that is now attached to the cord.
I laced the S hook into the loop on the elastic cord.
Once I let go, it holds the cord in place and allows for the doll's head to still have movement. I will just tuck that ribbon into the head just in case the S hook slips (which probably would never happen, but I like to play it safe.)
I went to the pharmacy, and bought a package of silcone ear plugs (which will not harm your doll. It's just like silicone putty that BJD owners use to put their doll's eyes in. It's a LOT cheaper if you buy this stuff instead of buying the putty from a doll shop that sells eyes. You can also go into a office supply store and buy stuff from 3M or Duck brands that is poster putty, and that works great too.) I mould a bit of it in my hands and then run it between the top of the head cap and her head. I do this in the front too. Serves two purposes---keeps the cap on, and holds wigs on nice too.
Hope this helped!