I saw accounts closed for abuse (there was the red cross and the text in their profile) that were still active (the green circle on their profile picture) some time after that happened (up to ~30 minutes)
Faire play
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It can take a small amount of time from the ban happening and the session to get removed
That's impossible, chess.com would immediately send you a message and the account is just closed.
It's not impossible. Some updates take a little bit of time to complete.