My prickly pear plant (Opuntia microdasys) fell over in the wind today and a paddle broke off. Luckily it was a clean cut so I decided to just drop it into a pot and hope it grows!
Also in the pot is an unidentified aloe cutting from the plant beside it. No clue what that is but it's been doing alright despite not being in the desert!
You've gotta let the broken end callus over before you can propagate succulents from leaves. Exposing the wounded tissue to soil before it finishes scabbing up makes it almost certain that you'll lose the leaf to fungi.
It only has a tiny cut cause the whole pad fell off at once, but I moved it out of the soil to try and let it scab over before planting it again!