While it's not the easiest thing to do, replacing you chalk bag cord may be inevitable after years of hard use.
If your cord is still in tack but is just needing replaced, tie one end to the new cord and pull it all the way thru until the new cord is thread all the way around the inside of the rim. Slide on the toggle than knot it off to secure the toggle.
If your cord is not in tack and is totally gone, you may want to tie a small bead to the end or just a doubled up knot. Than (very patiently) work the bead/ knot around the top of the bag by sort of inching the knot along. It may take a second but the reward of having a fresh new drawcord will be worth it, trust us.
1- Plastic Toggle
1- 19.5" 1/8" Nylon Paracord