i have an old apple id of which the email address is deleted now i want to delete the apple id but i cant logout of icloud be ause i have forgotten the answers to the security questions and the emailaddress has been deleted and now my id is locked

I have two apple ids one that I currently use and an old one that my sisters device was logged into a long time ago but now my sister wanted to creat her own Apple ID and her device is still logged into the old Apple ID on iCloud. We tried to log out of that old account the only problem is that the email address of that account was deleted a long time ago and now we can’t logout and I have also forgotten the answers to the security questions so now that old account is locked and we can’t delete it or disable it nor can we create a new Apple ID on that device .

So we are stuck and don’t know how to solve this issue.

please help us