As outlined in the post by MrHoffman, you have to have access to an account in order to request its deletion. Either that, or die and have somebody else ask. Or else just do nothing, though it may take some time for Apple to actually delete the account.
Legal - iCloud - Apple
IV. D. Upon receipt of a copy of a death certificate your Account may be terminated and all content within your Account deleted. Contact iCloud Support at iCloud - Official Apple Support for further assistance.
Legal - iCloud - Apple
VII. B "In addition, Apple may terminate your Account upon 30 days’ prior notice via email to the address associated with your Account if (a) your Account has been inactive for one (1) year