ok caseman, the guesses are right, dracaena marginata, tri-color. and yes, it is salvagable. you have 2 options, but as i have never had any luck with one of them, i would go with the second. the first is something called air layering. the second is this.
invest in some rooting hormone and using a CLEAN SHARP knife, finish severing the
plant at the break. strip the first 2 or 3 sets of leaves from the bottom of the top piece of
plant. dip it in rooting hormone and place it up to the first set of leaves still on in moist, good quality potting soil mixed with peat. cover the entire thing with a clear plastic bag to hold in the humidity and place in the same area where you have grown this very healthy
plant. it wouldn't be that big or pretty if you didn't have it in the perfect spot light wise. now, for the bottom, cut the "trunk" into 2 inch logs and place length wise in a tray.
click here for a previous discussion and pictures Nikkal, one of our other members was very helpful to me in a similar situation! good luck.