When we first had our large enclosure installed, the person "in charge" was HOT GLUING (grr!) the chrysalis' to metal file holders on a cheapo computer desk that was put inside as a work station. Well, not only did most of the first emergers fall to their deaths because the metal was too slippery to hold onto, but this person also ruined several chrysalis by burning them with the glue gun!
I've since taken over to some extent and put an end to the glue gun. What I do now is use a bit of thread and tie the chrysalis' to this big dead tree branch I found. When it's filled, it looks like a Christmas tree. Now when the butterflies come out they have this nice porous wood to hold onto. Our butterflies need to have this branch because a lot of our landscapers don't know any better and are always spraying the ground inside the enclosure when they water the plants. So if a butterfly falls down, they get too wet to climb up and end up dying. Luckily, I've had way less deaths since the branch has been installed.
I will usually remove a chrysalis to the tree branch if I find it on a leaf that's being slowly eaten away. Sadly, we actually weren't quick enough this morning and just as we spotted it, the caterpillar tooks it's last bite and the chrysalis went splat on the ground. I figured it was fairly new, too, since it was so wet when it broke open. Poor thing.