Answer: It sounds like you have Aeonium arboreum atropurpureum. This interesting plant can reach a height of 3' or more!
If the leaves are dropping off at a fast rate, it sounds like something is wrong. Do you have the plant in a sunny spot? This plant require good light and at least some direct sun. If it is in a really sunny spot, it's possible that you aren't giving it enough water; however, usually the problem with succulent plants is that they get too much water, especially during their dormant period.
I suggest you wait and see what happens. If the soil is bone dry, give it some water. I suspect it's suffering from the shock of moving from greenhouse conditions to your home. Hopefully, it will make a full recovery!
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