No matter what mix it's in it doesn't change a plants cultivate. It's an Echerveria of some type and would agree that it's a very special and might be a rather unique cultivate too. Perhaps it's Echerveria Sub.Sp A little overpotted Cv. Wont fair well in mud ?

The pot isn't really too small (could repot into just a bit bigger), but the plant sits too low inside of it - needs more 'soil'. All succulents (regardless the name) need good drainage, plenty of light and good air circulation. You could grow it inside, but need to give it as much light as possible, most of the times there isn't sufficient light for succulents (they will live & grow, but likely will etiolate because of not enough light). I believe that's original soil - it will be best to repot into much better draining potting mix. I see some yellowing leaves & that could be sign of waterlogging, & may cause rotting. Rosette type succulents grow leaves from the center. It could be one of the Echeveria agavoides.

really pretty =D Google graptopetalum or graptosedum to compare until you find the correct cultivar for your awesome little plant. Don't toss those fallen leaves, leave in pot. Each one has the potential to produce another plant. The ones that are squishy and gross are rotted, um, not those =) they will need to be discarded. The shrivelled beyond recognition ones won't either. The cache pot, while pretty and certainly breaks up the boredom, keeps too much moisture around roots, your plant will eventually start showing signs of distress. Ditch the cache pot. If you did not re-pot as yet, I would. The soil it is sold in is not appropriate for long term care and not associated with longevity of succulents. You can get bagged succulent and cactus mix, and then amend 60% perlite, 40% mix. When you water, fluid should just run as freely as it does when you turn on the tap. Not only does this help flush dissolved salts through the soil, but it ensures your entire plant's root system gets all it needs. The amount of perlite you add, directly results in a very airy mix. Roots need air and water, but not too much of each. This mix is a combination thatwill do nicely. Many people, including myself, use mixes that don't contain soil....looks like this: That is not top dressing, that is the actual potting medium. I find straight pumice to be easiest, and best for plant health, but it may be hard for people not in the US to procure. On an unrelated note, I had this one, here is how it appeared up until last night -___- It looks similar to yours, except it's tint is more blue-ish purple, where yours has a rosier blush, but, no matter. It is a crested form of a similar plant as yours. It was planted in the ground (not by me) in sandy soil and, see that little black upside down teardrop spot on the left of the stem?....rot =( Took 3 weeks to work it's way through the middle of the stem and then upwards. I didn't think much of it, but I should have been more diligent. It was not mushy, but the discoloration should have clued me in that something was wrong. Luckily, as a succulent, I have options to save this plant. I cut off all the rot and re-rooted the parts of the plants that were not black and mushy, It is now resting in the open air to dry up before I pot, lest it rots again. I saved all the leaves and they are also resting in open air, waiting for their chance to throw roots. That is only one scenario that can happen if left in unamended soil, unless you live in an area with the correct natural environment. It is also why, here in NY, I grow all my plants in a mix similar to what is pictured above. The plant pictured above, spent the summer planted in the ground in Ohio. Seller decided to dig up and sell on ebay when cleaning up the yard, preparing for winter. Anyhow, good luck with yours, as you can see, I really like these grapto typs =D

it looks like a very green perle von nurnberg. It's most likely an echeveria. Looks like it lost all of its leaves at the top... what happened to it?