Typically, the Member Card is held by a unit that the player can either kill or recruit. In The Binding Blade, for one, the Member Card is held by Hugh, a recruitable Mage who starts out as an enemy unit in Chapter 16.
In the localised versions of Shadow Dragon, the Member Card has been renamed to the VIP Card.
Of note is the fact that the chapter during which the Member Card is obtained usually features a
Secret Shop that can be accessed when it is held over the relevant tile.