There are certainly occasions where you can be stuck on a chair lift for a period of time, hopefully you’re not forgotten and left for the week, but a mechanical failure or other emergency my cause you to be stuck for a time.

I'm not sure about packing equipment specifically for a chair lift emergency, but my general skiing equipment includes a "space blanket" type bag and high energy food snacks and when I’m in the snow I always have some extra clothing.

Alerting authorities, shelter and food are probably the priorities.

After reading through the discussion I’ll make a point of adding the ski resort’s emergency phone numbers to my contact list (in addition to general emergency numbers). Then (hopefully) I can phone up and ask what’s happening and how long.

Re paracord rappels. I think (as was mentioned) you may be able to use some cord to get you a bit lower to the ground (before you jump/fall), but if you were high up it would seem foolish.

BUT after speaking to the resort management you could lower your paracord to the ground ask management to tie on some supplies – food, clothing, blankets. (I guess you could also use it to pull up a proper climbing rope, but I really don’t see this ever happening)