I worked somewhere that when people quit or were let go it was a BIG secret. Nobody was allowed to mention that they left, if you were caught discussing it you would get in trouble.
We'd be in meetings like, "where's Jeff? Will Jeff be joining?" and there would be awkward silences because nobody could tell them he would never be joining because he was gone.
All it did was create a ton of gossip and rumors. Not a great policy!