You will have to add the password security before the document is signed, not afterwards. If you need it to be afterwards, you could use the security envelope feature of Acrobat, which essentially will include the signed document as a file attachment to a secured envelope PDF. You can use either password security or certificate security. The latter may be a better choice.
Thanks George, I thought that was going to be the answer but I wanted to make sure. I will give it a try and let you know.