They all can be started from cuttings but you have to get rid of the rot first. Cut them (with a very sharp knife - not clippers) until the stem is clear of any rot. Let them sit on the counter for a few days until the cuts scab over then stick them in almost dry/barely damp cactus oil and wait for roots.
The one with a lot of pups in a Sempvivum. They grow pups, bloom and die so don't worry about the central rosette but root the pups.