Once they find a suitable spot, they spin a silk pad, attach themselves upside-down in a “J” shape, and begin the transformation into a chrysalis. Spinning, elimination of waste from their gut, and other changes take about 24 hours before the chrysalid emerges.
I have found very few chrysalids in the wild, because they are so well concealed.
When caterpillars go missing
I've heard so many stories from people who raise monarchs, about missing caterpillars. Suddenly, a butterfly appears out of nowhere in their house. Or they are surprised to find a chrysalid concealed in the drapes or under a table.
Once I took caterpillars to an event where children could handle them. On my short trip home, I didn't bother to count the caterpillars or cover the bin... mistake!
About 10 days later while driving, I was startled when a monarch flew past my field of view. I nearly slammed on the brakes, thinking it was going to collide with my windshield. But then it flew past my head... and I realized it was inside the car! The caterpillar had escaped into the car while being transported. Perhaps it wasn't ready to form the chrysalis (pupate). But faced with starvation, it did just that.
It was summertime, and I don't keep the car in a garage. Temperatures inside the car should have reached lethal temperatures, and the chrysalid could also have died of dehydration! I suspect it moved away from light--causing it to descend where temperatures were much lower, perhaps under a seat. It wasn't just luck that it survived... because two days later, another butterfly surprised me while driving!
Here's how I avoid that surprise
I raise caterpillars in a large bin, on a card table that has a layer of newspaper turned up at the edge of the table to keep the frass on the table. When a large caterpillar starts to wander, I put it back on a milkweed (to be sure it's ready to "J"). If I see it wandering off the milkweed again, then I put it into a small bin with an old manilla file folder loosely affixed to the top. This lid keeps them confined until they form the "J."
Caterpillars rarely escape in my house because they tend to wander around the rim of the bin. If they get to the table top, they wander around the rim of turned-up paper. If they descend further, they find the underside of the card table dark and stable--the perfect place to form a "J."
If you are out of the house for long periods, you may need to place a lid on the large bin while you are away.
The first half was sourced from CoPilot AI, edited.