As hens and chicks grow, their bottom leaves will shrivel up and die. Sometimes this is caused by overwatering, underwatering, not enough light or other stresses to the plant. Other times though, it is just the variety. Some varieties have lots of leaves die back during the winter while others lose hardly any.
It isn't necessary to remove the dead leaves, but it does a lot to help make the plants look pretty again.
Removing the dead leaves from hens and chicks is fairly easy. The time required will depend on how many plants you have. If you are going to clean up your plants it is best to do it in February or March, before the spring growth starts. If the rosette is already sending out runners for chicks then you run the risk of pulling those off with the dead foliage.
Just grab as many of the dead leaves as you can and pull to the side. The should pop off easily. This can be done with the rosette still planted.
You'll end up with a pile of dead leaves and a plant with a bare trunk. If there is a lot of dead growth then you may want to replant your sempervivum so that it isn't growing up on top of a stalk. If this is the case, just work the plant down deeper into the soil so that the stalk is covered.
It's really simple and it will leave you with a hen and chick plant that looks fresh and brand new... ready to produce offsets in the spring!