There isn't only one thing that can happen to an exoskeleton on a growing arthropod. For some arthropods, such as spiders, the exoskeleton grows as they do. For some other arthropods including crabs,...
As the arthropod grows up, the exoskeleton sheds in order for the arthropod to grow inside of it.
It moults and sheds it. A new, soft one inside expamds and hardens immediately to a form a larger exoskeleton.
Carapace
No, The animal sheds out of the exoskeleton.