In the Harry Potter series, Dobby the house-elf is unable to be healed because he was under the control of a powerful wizard and was forced to perform magic against his will. In the books, it is explained that when a house-elf is forced to perform magic against its will, it becomes severely weakened and can eventually die as a result. Additionally, in the final book, it is stated that Dobby was mortally wounded by Bellatrix Lestrange and did not have time to be healed before he passed away.