Do you mean they no longer have access to that email account as well?
If you try to rest your password then usually they will use that email address for the reset so you need access to that.
Otherwise, if you want to change your password and if you are signed into icloud and if you know the passcode for the device and you have access to that email account you should be able to do it.
It's been a while but I did do something like this for my mother in law.
Usually, when you set it up you have to answer a couple of security questions like what was the name of your first pet etc. If you know or can guess the answers you can also usually reset the password (if it still works that way).
In any case, don't sign out, try to change the password or use the 'forgotten password' procedure and see how you get on. You should be able to bail out before anything permanent changes.
Otherwise, yes you need to ring support but they'll probably likely still ask you the security questions.
