iCloud restore "Enter Old Passcode" An iPhone 6 Plus' Touch ID stopped working and the user couldn't remember the passcode and, after many failed attempts, was forced to choose between setting up as a new iPhone or restoring from backup.

The iPhone 6 Plus was frequently backed up by iCloud and never backed up by iTunes.

Directly (from the initial setup) or indirectly (once setup as a new iPhone), attempting to restore from iCloud  prompted for and accepted Apple ID authentication (username, password, and phone number-based TFA) then prompted as follows and rejected all given:


  Enter Old Passcode
  
  Passwords, home and other data are protected by the passcode
  previously used to unlock this iPhone.
  
  Your passcode is encrypted and cannot be read by Apple.


I wasn't able to find anything online regarding this scenario, hence this post.
I contacted Apple's technical support who said:


  At this point then we won’t be able to get past the passcode unless you manage to remember it at a later point in time
  
  The only way around this would be use the phone as new, and then sync with iCloud contacts, calendar and Photo library if you use those.


Personally, I have restored from iCloud and I was never prompted for my passcode so I guessed that it was prompting from a verification point-of-view, rather than an encryption point-of-view.

On an iPad, I enabled iCloud and signed in using the same Apple ID.

On the iPhone, restoring from iCloud prompted for a verification code from the iPad and succeeded.

Apple's technical support said:


  Oh perfect, you should be working here, haha