We can confirm, based on the type of skeleton and lack of a respiratory organ, that a worm will die if it dries out due to the fact that the exchange of gases happens through the mucus on its skin.
As stated in the question, Earthworms do not possess any form of respiratory organs. To account for this, they have evolved the ability to breathe through their skin. This ability is due to what is known as a hydrostatic skeleton, possessed by most annelids.
This skeleton is covered in mucus and allows the exchange of gases with its surroundings, therefore, if the worm were to dry up, the mucus that encases the skeleton would harden and thus prevent the interchanging of oxygen and carbon dioxide. Effectively, the worm would not be able to breathe and would die.
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