Yup, the process of shedding it is called moulting. A new bigger
exoskeleton would form soon after. Both the crab and cockroach
exoskeleton contains chitin to strengthen it.
It is rather interesting to study other creatures of life, isn't
it. Talking about creepy crawlies, spiders have a sort of hydraulic
system to help move their legs, thats why dead spiders always have
their legs curled inwards. Fluid is used to pump into the legs to
spread it out while muscles help contact it. When the spider loses
too much fluid, it doesn't have enough to spread out its legs.
