The only time I've seen anything along those lines in the field is if Unity is configured to dial out for message notification and you get a "collision" which results in a conference between a Unity port and an incoming call and the phone being dialed for notification (i.e. the subscriber's work phone). It would normally start with the "please enter your Id" though, it'd start with "this is the Unity messaging system calling with a message for (voice name of subscriber)" if that were the scenario. this would only happen at the begining of the call, as well, not in the middle of a conversation.
Any chance there's some sort of weird conference bridging thing with the subscriber's phone that's causing it to dial Unity as a direct call while they're on the line and conferencing it in? That would result in the prompt you're reporting - Unity's not going to jump into the call on it's own (and can't unless you have some sort of barge in feature setup) - it would have to be something being done by the local subscriber on the call that would cause this.
Maybe someone was getting cute and trying to figure out how to do a live record scenario from the phone where Unity is dialed as a conference member and will start to record - if the user's mailbox has a phone password you'd hear just what you're reporting. Just a thought.
