As with the entire plant, hens and chicks flower care consists of neglect. You can leave the bloom until it has finished and the stem and base rosette will dry out and die. Clip off the stem rather than pulling it out of the living cluster or you may end up yanking some of the precious offsets. You may also choose to let nature take its course and leave the dying stem as proof of an interesting life cycle, which will eventually break off and compost in the area. The young chicks will grow larger and fill in any gaps the parent plant made when bidding its fond farewell to this world. So enjoy the flowers and the guarantee of everlasting life this plant has in its offspring.