Thanks @oldturkey03 :) @mike85647 It's probably best to reinforce the part where the drawstring is wearing through. You could either sew a strip of fabric onto it (should work similarly to the procedure of sewing a patch onto a pillow, see my guide [guide|162810|here]), or attach a strip of sticky fabric. There are iron-on fabrics and patches you could use, in that case be careful not to melt the fabric of your jacket if it's made from artificial fibers like nylon or polyester - put a tea towel or a sheet on top before you start ironing.
But you can also get stick-on patches that you don't have to iron on ([link|https://www.naehplatz.de/Prym-Klebeflicken-Nylon-10-x-18-cm-braun|this one] is an example in a German store), that would be better if your jacket is made from nylon, polyester or other artificial fibers. If your jacket is mostly cotton, an iron-on patch should work fine.
Just to be sure, could you upload a picture of your jacket?