Separate the broken top from the plant. Use a new razor blade, utility knife blade, or scalpel to clean up the break on the rooted part. There are axillary buds immediately above each leaf and leaf scar (where the leaf was attached to the stem). You'll be depending on them to produce new branches. Wait until the wound stops weeping, then coat it with waterproof wood glue. This will stay the wound from drying out and dying back. It will soon start pushing new branches, much like this Aeonium did after it was purposely truncated to achieve the effect you see:

Second, clean up the wound on the unwilling propagule with whatever sharp tool you used on the rooted part. You can dip the proximal end in a fungicide if you like - flowers of sulfur works very well. As you clean up the wound, the idea is to remove bruised tissue and make sure there are no shredded fibers attached to the wounded area - like a pair of scissors or dull tool would create. I buy disposable scalpels (which I use over and over) to prepare propagules for cloning. Use the tool to cut leaves off the stem from the bottom up. Leave the top 3-4 new leaves on the propagule. Let it rest for a few days at room temp on a paper towel or sheet of paper. Stick the prepared cutting in a very fast draining medium and barely moisten the medium. An occasional spritz to the top of the medium is all you need. When you see the propagule pushing new growth, you can treat it as you normally would.

Cleanliness and attention to small details can make a very large difference in success %s.

Al