iPhone 6s iCloud defaults to old Apple ID. Can't delete iCloud account because it says Apple ID is wrong
The ID still exists, &amp; in fact cannot be deleted - Apple apparently keep them 'forever'. 

What you can do is change the primary email address attached to the ID - the ID itself doesn't need to be a valid email address, it's merely a sensible starting point.


  Change your Apple ID 
  
  Learn how to change the email address that you use as your Apple ID.
  
  In most cases, your Apple ID is also the primary email address of your Apple ID account. You can change your Apple ID to any other email address you control, as long as it's not already in use as an Apple ID. If your email address ends with @icloud.com, @me.com, or @mac.com, it's already an Apple ID. 
  
  Use these steps to reset your Apple ID:
  
  
  Sign out of iCloud, the iTunes Store, App Store, FaceTime, Find My Friends, Find My iPhone, and iMessage on each device that uses your current Apple ID for these services.
  1.Go to My Apple ID.
  Select Manage your Apple ID and sign in. Forgot your password?
  Select Edit next to Apple ID and Primary Email Address.
  Enter the email address that you want to use as your Apple ID, then select Save Changes. Apple will send a verification email to that address.
  Open the email from Apple, then click Verify Now. Didn't receive the email?
  When the My Apple ID page opens, sign in with your new Apple ID email address and password. When you see a message that verification is complete, you can start using your updated Apple ID.
  Update the features and services that you use with Apple ID, so that each one is using your updated Apple ID.
  
  
  If you need to change the Apple ID that's signed in to your iOS device, use these steps to sign out, then back in with a different Apple ID.


Ref: Apple KB - Change your Apple ID