Inserts usually break at the weakest point, the hole where the pearl slots in. The problem I've found is that when an insert breaks they tend to 'grow' slightly. and can be a devil to refit to an insert (using glue or whatever). Something akin to the way the belt on my trousers keeps my beer belly neatly in check ... but out it pops as soon as I undo my buckle
My engineering skills are fairly raw but I'm thinking the odd way a broken insert suddenly seems to be a squilli-meter larger than it was before it broke, is what engineers might refer to as 'cross-sectional distortion'. Bend, twist, break, cut or fold a piece of steel and it stretches. I had to learn about it 25 years ago when I was making up window frames from stainless steel 'U' channel for an old sports car. Gentle curves were easy but anything involving a tighter curve, or a cut (or similar) just distorted the steel. That engineering problem was ultimately solved with slots being cut, filled with stainless welding rod and a long afternoon on the flapper disc.
Anyways, much less drama with a broken insert. If you are very lucky, you might simply have success refitting a broken insert to a bezel, using the simple 'glue and spring-loaded clothes peg' trick. The bad news ... I have never used that trick and successfully re-fitted a pearl. I'm thinking a clever watchmaker working with a broken insert might do very judicious work with a dremel to ease the fit a bit and get you up an running again with insert and pearl fitted . With early inserts now running at $2k / $3k plus it's certainly viable to fix 'em ... but you want the right guy on the task.
Good luck !
Edited for typos, poor grammar and generally sloppy conveyance of my message.