Dashagriva's brothers Vibhishana and Kumbhakarna also prayed to the gods for boons.
Vibhishana was an unusual rakshasa: he revered dharma, righteousness. Vibhishana thus prayed that he always uphold dharma, and Brahma granted his prayer.
Kumbhakarna, however, was a monstrous giant, and the devas feared him. At their request, Saraswati, devi of wisdom, confused Kumbhakarna's tongue when he asked for his boon: instead of Nir-deva-tvam (death-to-devas), Kumbhakarna asked for Nidrava-tvam (sleepiness).
As a result, Kumbhakarna was awake only one day each year. If anyone dared disturb his sleep before the year had passed, Kumbhakarna was fated to die that same day.
Inspired by: The Ramayana (Uttara Kanda: Sarga 10).
Notes: In some versions, Kumbhakarna wanted to ask for Indra-asana (Indra's seat), but instead Saraswati made him ask for Nidra-asana. Nidra means "Sleep" and Nidra is the name of the Goddess of Sleep.