How I might Sign out from a deleted Apple id!

Since you posted the ID has already been deleted, this may not work.  If you are the original owner, contact Apple. They may be able to remove the Activation Lock if provided the required paperwork. Either take the device, the original purchase receipt with the serial number, and a photo ID to the nearest Apple Store (if it has reopened)

Genius Bar Reservation and Apple Support Options - Apple.    

or contact Apple ID Support. 

 Apple ID - Official Apple Support.    

Contact Apple for help with Apple ID account security - Apple Support.  (Link doesn’t always load)   

Get Support      Work through the screens to get a chat option. 

Apple Support schedule phone call

https://twitter.com/AppleSupport       People have posted it may take an hour or more to get a response.

You won't be able to sign out of a deleted ID. But you can try to stop deletion. See below. Having stoped the deletion you can deal with your problem.

How to Delete your Apple ID Account https://support.apple.com/en-us/HT208504 

“While your request is being processed, you can contact Apple Support with the unique alphanumeric access code you received, and we’ll help you cancel your request. After your account is deleted, Apple can't cancel the request, reopen your account, or restore your data.” I see that you apparently have the code.

If it's too late to stop deletion and your problem persists, post back and explain exactly what you are doing when the ID becomes a problem.