How are wet clothes and a depressed person alike? One gets hung up to dry, the other gets hung up to die.
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Explanation
The joke plays on the double meaning of "hung up." Clothes are hung up to dry, which is a normal process. However, someone who is depressed might "hang themselves" to die which is a grim situation, thus making the joke dark and morbid. The humor comes from the twist of using the same term for such different scenarios.