Other than "to emerge", "to come out" or "to climb out", is there a specific verb that means "to emerge out of a chrysalis" or "to emerge out of a cocoon", like there is "to hatch" for "to emerge out of an egg"?
You might be looking for eclose:
(of an insect) emerge as an adult from the pupa or as a larva from the egg.
From wikipedia, emphasis mine:
Like other types of pupae, the chrysalis stage in most butterflies is one in which there is little movement. However, some butterfly pupae are capable of moving the abdominal segments to produce sounds or to scare away potential predators. Within the chrysalis, growth and differentiation occur. The adult butterfly emerges (ecloses) from this and expands its wings by pumping haemolymph into the wing veins. Although this sudden and rapid change from pupa to imago is often called metamorphosis, metamorphosis is really the whole series of changes that an insect undergoes from egg to adult.
If you do a google image search of eclosion (the noun form of the verb eclose), you get a bunch of pictures of butterflies coming out of cocoons, so I think this is as close as you're going to get.
Edit: Josh61 has downvoted me for not providing usages from academic contexts (I was unaware that was a requirement on this site, my bad), so here are a couple examples:
Eclosion is the stage in development when the adult insect emerges from the shell of its old cuticle.
Fruit flies proceed through a series of characteristic developmental stages, beginning with the embryonic through a series of three larval stages to a pupal stage from which adults emerge or eclose.
You can do a search on Google Scholar if you really want more.
I think that hatch can be used also for cocoons and chrysalises:
- (Zoology) to cause (the young of various animals, esp birds) to emerge from the egg or (of young birds, etc) to emerge from the egg
- (Zoology) to cause (eggs) to break and release the fully developed young or (of eggs) to break and release the young animal within
Hatching and releasing a butterfly from its cocoon is a fun and educational process for kids (and adults) to observe.
Creating a safe environment for a cocoon to hatch into a butterfly is very easy. Simply tape a string across a jar full of grass or bucket and hang the cocoon to the string using a separate piece of tape via the string-like substance at the top of the cocoon.