Alex said:
Climb out with only rope? Well if you have some friends up the pitch I guess you tie a harness and your mates haul you (unless there gear is gone too!). With more than one rope (other than the pitch rope) then you can make a harness and prussic knots I guess.
The idea is you and your group decend into the cave. Drop your vert gear and do the caving. Come back, and all your gear is GONE. How do you get out? And yes I have heard of instances where this has happened so it's not completely insane scenario. Pack rats...other group comes in and gear gets mixed up and taken out by accident...prank...
I'm giving away the answer hence the nsfw tag to hide it for those who don't want to see it, but spoiler is safe for work! And no second rope. You just have the end of the rope rigged. Stuff you ALWAYS carry in your pack is fair use though.
[nsfw]I always carry 20-ft webbing and carabiner in my pack, so there is my nice Swiss seat harness. Use the end of the rope to tie a Blake's hitch - works like prussik but on - and this is key - same diameter of rope and is tied with the end of a rope. Blakes is your progress capture. You'll have to footlock to stand up, slide up the blakes, sit down, re-footlock, stand up sliding up the Blakes, rinse and repeat.
It fucking sucks and not everyone will be physically able to do it (I did a few barely successful cycles, but some can climb for 100-ft that way!) - but if you're stuck in the pit, only one person has to get out!
If you do not have a webbing piece, use a rock to bash off a bit of rope end for a seat harness to be tied. [/nsfw] Cavet is - I'm not sure if the solution would work with a rebelay.