This is a type of Sempervivum (commonly called Hens and Chicks as you mentioned). The shoots coming off are the “chicks.” This is how it propagates new plants. You can pull them off the mother plant gently, and plant them in their own pot.
It looks as though your Semp isn’t getting enough light, which is why those shoots are so long and don’t have much of a rosette on them yet. They are growing extra fast right now because the “hen” has died. This is completely normal.
Sempervivums are monocarpic – this means that they only flower once, and then die. This is most likely what happened to the main plant in the picture. The chicks that have brown leaves and are dying could be underwatered. Remove them from the arrangement and plant them in a separate pot, and water as you would a full sized plant.
Most importantly though, you should move the pot (gradually) to somewhere that gets more sunlight or look into getting a grow light if they are indoors. They won’t revert back to being more compact, but the new growth will form in a much more tight rosette and resemble the other chicks more.