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If the old cookie has a different name than the new cookie that’s easy, make a plugin to set the time for it in the past.

If it’s the same cookie name old and new, and it’s a problem of the hash for the value inside being wrong, there is nothing you can do.

If you can detect when a cookie is being sent but failing to authorize you could delete the cookie like the first method I mentioned. You’d have to replace a function or two from pluggable.php