Photo confused me - I thought you are asking about plant with purplish leaves...

Is there a drainage hole in your container?

What is the potting mix/soil like?

there are a few photos of the plant, it is the lighter green one that I am more concerned about. there is no drainage hole in the container. Since the arrangement was a gift I am not positive on the soil but I believe there is a layer of rocks to create drainage at the bottom of the planter then a layer of top soil and decorative rocks over that.

the light green plant has gotten much smaller that it originally was, and the stem is now shriveled and dry (you can see this best in the first photo)

Unfortunately I live in a small dorm room and have very few options for light, I have had the plant placed in the area that will receive the most light throughout the day. I could easily change out the soil in the pot, but I am afraid that if I use a pot with a drainage hole that I will make a mess in my room. Most of the articles I have read have said that you can use a pot without a drainage hole, but that you will have to be more careful and less frequent with you watering.

You can't, the plant will eventually die from it, as it can't drain properly or get oxygen to its roots.

Just place a saucer under the pot, most of us do that (I'd guess). I use plastic lids from pints of ice cream; look for a cover of a jar that's the right size to fit underneath. It'll collect any water (dump it out after a few minutes) & loose bits of soil. Just place a piece of newspaper inside the pot to hold the soil in, works fine.

Marisa

You could always get a light (best wold be perhaps a CFL or LED lightbulb - LED emits very little heat) and have it on timer for some hrs/day.

Karen is giving you great suggestions - with succulents, it is all about drainage (and light). Watering less and/or less often is not really best solution - it may work temporary - but plants still need some water (at appropriate times) and will look best with that kind of care. Layer or rocks doesn't solve drainage either - excess water collects between them, and creates conditions that could be too damp for succulents. It is unfortunate that arrangements are often sold in those kind of containers - they usually look great, but do not provide best growing conditions for plants.

Oldest leaves will usually dry up and fall off, but shouldn't be too many at the same time. If plants are in container and soil with poor drainage, they often either rot, or dehydrate from lack of some/proper watering.