That's not a feature of a!cardLayout(). You could potentially accomplish a similar effect with a!boxLayout(), though.
Also note: there's nothing keeping you from implementing something like this in a!cardLayout() - manually, for yourself. You could have a Rich Text Icon in your card somewhere which, when clicked, hides all contents of the card (other than a "reopen" icon). That wouldn't be very difficult to do, wouldn't require any unusual workarounds, but isn't a built-in feature.