Not that I expect HP to do anything ... And not that I can do anything myself ... But how would we like such a feature to work?
I would say:
If there's a card already open, it stays accessible.
You still see notifications from secured apps.
To launch an app, from the launcher or a notification or another app, you must enter the password.
To designate an app to be secured, there's some new Settings app, similar to Accounts, where you toggle it on. I suppose this app has to be secure too, if any other apps are. Not just Email and Messaging, but any app.
A frequent request is to secure certain photo albums. It'd be convenient if the same settings app could be used to designate such albums.
Maybe we should be able to designate certain accounts as secure while others are open ... although I don't see a compelling use case yet.