How to remove your xBox account
You’ll have a generic MS account if you created one at one of their MS services. E.g. we had an xBox account too (so it seems) which is simply our Hotmail test account that belongs to MS too.
For more info, also see the MS Office entry at removemyname.com. Summarising: you can’t do it, so then the advice is to contact them by form, mail or telephone. Otherwise it may be enough to cancel the original account (perhaps a Hotmail or Live account). See the entry for those on removemyname.com too.
For cancelling xBox subscriptions see: http://support.xbox.com/en-GB/billing-and-subscriptions/subscription-management/cancel-xbox-live-gold-subscription
Cannot delete the account, or worried the data lingers? See what to do when a site won’t let you delete.