This doesn't happen for vinyl dolls, but lately I've come across some plastic dolls that have been damaged and the methods are very similar for repairing. Using epoxy glues and super glues can save a broken doll and in some cases keep it from incurring future damage.

This video was helpful to see reconstruction of a completely broken head Tips and Tricks of a Doll Head Reglue Using Epoxy with Stanley Strawn | Virtual Doll Convention (youtube.com)

This video was very useful if you apply the concept to repairing broken neck pieces but also can apply to fixing areas like leg holes, arm holes, where the plastic has broken or chipped away and it affects being able to attach a limb. The method uses crazy glue or super glue and then applying baking soda on top of it to build up the areas and make them strong enough to reattach the pieces. This can be particularly helpful if pieces of plastic have broken off and are not present and you need to rebuild an area. The only thing I do not like about this video is that it starts from the end and then as you watch the video you get an idea of what it looked like from the beginning so it's not chronological. But watching the technique is important https://youtu.be/1N9Fq5CWS7A?si=-AtOVks_IeJM-ikj

I found these two videos incredibly helpful for repair.