"I guess the question might be: How many people have died trying to rappel versus how many have died from being stranded overnight on a chairlift? I suspect the answer is several hundred rappellers and no chairlift victims."
I suspect that the real answer is no one, or almost no one has ever died trying to rappel out of a chair lift. Here is my reasoning.
Firstly, for the most part chair lifts are very reliable. In the event that they do stop working for more than the few minutes typical of loading/unloading issues, stranded riders are informed by ski patrol and mountain employees about the repair/rescue status so those contemplating self evacuation probably wouldn't bother to try.
Secondly, the few individuals who do actually carry self-evacuation gear probably now how to use it, such as ski patrol and mountain employees and know when it is acceptable to use. Lastly, I just haven't seen any comments on such a things in the news or online at any ski/snowboard forums.
What I have seen first hand and learned of in the news are injuries to people caused by jumping off of temporarily stropped lifts onto what they think is soft snow from what they thought, wasn't too high.
The whole, stranded on a chair lift (not enclosed tram/gondola) scenario is utterly silly to me, since at most resorts where I've patrolled or skied the standard practice is that when a chair is "closed", access is limited while the chairs continue to run and each chair is inspected. In some cases this means flipping seats up to limit snow collection and in other cases, just insuring that there are no passengers or damage to chairs.
Also, patrollers, groomers and other mountain workers are out on the slopes long after and well before the resort is closed and would likely notice someone stranded on a chairlift. Please note, this does mean they'll see you if you are stuck in a tree well, lost in a more remote part of the resort or out in the side country.
As a note, clearwater also mentioned his ski patrol organization carried self evacuation gear.