Banked Money and banked Hits are the only cards from the deck that can persist with a player from turn to turn. (Wounds also persist, but don’t come from the deck.)
A player with a banked Hit may spend three Money during the Money Talks phase to deal a wound to any player, which returns that Hit to the discard pile. Otherwise, the banked Hit persists in that player’s bank until used, or the game ends.
To help make it clear which cards are banked and which are in a player’s stack, slide banked cards partway underneath your role card. Other players are allowed to know what you have banked, so keep them fanned out, and don’t slide them all the way under your role.