Bitcoin QT wallet passphrase

What does Bitcoin-Qt “Change Passphrase…” do to existing private keys and corresponding addresses?

If your wallet hasn't been compromised (how can you be sure?) then it should be enough to secure it with a strong passphrase and then be sure to back it up.

If your wallet has been or even just might have been compromised then securing it with a strong passphrase now might not be enough. Sending the Bitcoins at risk to a new address in the same wallet generated after the strong passphrase is put into place might not even be enough. It might take creating a whole new wallet on a known to be uncompromised system (how can you be sure?) and securing it with a strong passphrase before using an address generated in it to establish security.

Backing up your wallet to a cloud, e.g. emailing it to a Gmail account, etc., puts it at risk. If you ever did this before securing it with a strong passphrase then you should really move to a new wallet. Deleting the pre-strong passphrase copies is an illusion.