This doesn’t happen too often, but it happens… The curb pin (that is the tiny little pin that sits on the regulator and limits the effective length of the hairspring) is broken off and needs replacing. When I took this photo, the curb pin was still there, but after the regulator came out of the cleaning machine, it was broken off – bad luck!
Having removed the left-overs of the old curb pin with a sharp blade (cutting off the riveted bit), I take a standard brass tapered pin (you can buy those on eBay), and put it in the lathe to slim the tip down until it fits into the regulator. Make sure you got enough length, so that the boot (that is the bit that holds the hairspring against the curb pin) just goes over the end of the curb pin when turned.
Now cut the tapered pin (you can see the cut bit in the bottom left of the photo), so that you still have a bit of pin sticking out from the regulator. With the tiniest hammer you can find, rivet the new curb pin to the regulator.
The new curb pin under the microscope. Once riveted into place, you have to adjust the curb pin so that it just holds the hairspring tight enough so it won’t move from the boot to the curb pin and back when the balance is turning, but not too tight so that the hairspring can still slide through the gap when adjusting the beat rate.