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"I'm raising Monarch caterpillars inside, and the last two times the caterpillars formed a J and went to shed their last skin, the skin did not fully come off, and the chrysalis did not fully emerge, only the very bottom of it, and they both died before the skin fully came off. Only the very tip of the green chrysalis could be seen, with the dead caterpillar was dangling there with most of his skin on."
I assume your caterpillar/pupa looked somewhat like the first photo. Several things can cause this. According to Dr. Urqhart, a silk strand caught around the J'ing caterpillar can cause it. Sometimes it is simply too weak or it may have other problems. This is common. It is heartbreaking, but it happens a lot.
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"Underneath one of them was a little puddle of green fluid, and the other one's abdomen seemed very squishy and liquidy, like there wasn't a chrysalis to come out, only liquid there."
Look at the second photo. The green fluid is blood. Another caterpillar crawled on this one and tore the skin slightly before it pupated. When it was pupating, it pupated at the tear which resulted in a deformed pupa.
It IS squishy. This is normal! When it first pupates, it is basically gel with a cuticle. This gel is already preformed in some ways - you can see the antennae, legs, proboscis, wings, and more. Note the photo with these parts labeled. After an hour, it will have slowly reshaped into the classic Monarch chrysalis shape.
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"I had touched both of them one time to get them back into the cage because they wandered off, but just by letting them crawl on a piece of paper and putting them in there. What do you think happened?"
It is safe to touch caterpillars if YOU ARE GENTLE. If one has started laying a silk mat, it should be left alone. If one leaves the plant in a rearing container and has not escaped the container, it should be left alone. They leave to molt (and should be left alone) and they leave the plant to pupate (and should be left alone). They can find their way back as long as they are inside the container with the plant.
"I'm very upset and I've been doing everything I can to keep these caterpillars healthy!!! Any suggestions you have would be really appreciated."
First, realize that butterflies have a rough time in nature. Most likely the problem is NOT your fault.
Nature is deadly. Only 1 or 2 out of 100 eggs will become an adult butterfly. Disease is a serious issue in nature. Between predators, parasitoids, disease, windshields, weather, and more ... very few become adult butterflies.
Because of the prevalence of disease in nature, ALWAYS disinfect a rearing container between batches of caterpillars. If your last batch of caterpillars did fine, still disinfect the containers and everything else that you touch or touches caterpillars. It is safest.
Enjoy and please let us know if we can do anything to help you.